In this paper, we define robust weak ergodicity and study the relation between robust weak ergodicity and stable ergodicity for conservative partially hyperbolic systems. We prove that a C^r（r 〉 1） conservative par...In this paper, we define robust weak ergodicity and study the relation between robust weak ergodicity and stable ergodicity for conservative partially hyperbolic systems. We prove that a C^r（r 〉 1） conservative partially hyperbolic diffeomorphism is stably ergodic if it is robustly weakly ergodic and has positive （or negative） central exponents on a positive measure set. Furthermore, if the condition of robust weak ergodicity is replaced by weak ergodicity, then the diffeomophism is an almost stably ergodic system. Additionally, we show in dimension three, a C^r（r 〉 1） conservative partially hyperbolic diffeomorphism can be approximated by stably ergodic systems if it is robustly weakly ergodic and robustly has non-zero central exponents.展开更多
In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of（pt）t≥0 to...In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of（pt）t≥0 to equilibrium uniform on any bounded subset in H.展开更多
In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a...In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a quasi-birth-and-death process. As a byproduct of V-uniform ergodicity, we derive computable bounds on the exponential moments of the busy period.展开更多
In this paper, we propose a new one-time one-key encryption algorithm based on the ergodicity of a skew tent chaotic map. We divide the chaotic trajectory into sub-intervals and map them to integers, and use this sche...In this paper, we propose a new one-time one-key encryption algorithm based on the ergodicity of a skew tent chaotic map. We divide the chaotic trajectory into sub-intervals and map them to integers, and use this scheme to encrypt plaintext and obtain ciphertext. In this algorithm, the plaintext information in the key is used, so different plaintexts or different total numbers of plaintext letters will encrypt different ciphertexts. Simulation results show that the performance and the security of the proposed encryption algorithm can encrypt plaintext effectively and resist various typical attacks.展开更多
At low temperatures the configurational phase space of a macroscopic complex system （e.g., a spin-glass） of N - 10^23 interacting particles may split into an exponential number Ωs - exp（const × N） of ergodic...At low temperatures the configurational phase space of a macroscopic complex system （e.g., a spin-glass） of N - 10^23 interacting particles may split into an exponential number Ωs - exp（const × N） of ergodic sub-spaces （thermodynamic states）. It is usually assumed that the equilibrium collective behavior of such a system is determined by its ground thermodynamic states of the minimal free-energy density, and that the equilibrium free energies follow the distribution of exponentied decay. But actually for some complex systems, the equilibrium free-energy values may follow a Gaussian distribution within an intermediate temperature range, and consequently their equilibrium properties are contributed by excited thermodynamic states. Based on this analysis, the re-weighting parameter y in the cavity approach of spin-glasses is easily understood. Depending on the free-energy distribution, the optimal y can either be equal to or be strictly less than the inverse temperature β.展开更多
Let X be a compact metric space and C（X） be the space of all continuous functions on X. In this article, the authors consider the Markov operator T ： C（X）N C（X）N defined by for any f = （f1,f2,… ,fN）, where ...Let X be a compact metric space and C（X） be the space of all continuous functions on X. In this article, the authors consider the Markov operator T ： C（X）N C（X）N defined by for any f = （f1,f2,… ,fN）, where （pij） is a N x N transition probability matrix and {wij } is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T＊-invariant measures where T＊ is the adjoint operator of T.展开更多
The finite data estimates of the complex fourth-order moments of a signal consisting of random harmonics are analyzed. Conditions for the fourth-order stationarity and ergodicity are obtained. Explicit formulas for th...The finite data estimates of the complex fourth-order moments of a signal consisting of random harmonics are analyzed. Conditions for the fourth-order stationarity and ergodicity are obtained. Explicit formulas for the estimation error and its variance, as well as their limiting large sample values are derived. Finally, a special case relevant to cubic phase coupling is considered, and these results are stated for this case, the variance is shown to comprise an ergodic and a nonergodic part.展开更多
The IP P＋M/M/c queueing system has been extensively used in the modern communication system.The existence and uniqueness of stationary distribution of the queue length L（t）for IP P＋M/M/1 queue has been proved in[1...The IP P＋M/M/c queueing system has been extensively used in the modern communication system.The existence and uniqueness of stationary distribution of the queue length L（t）for IP P＋M/M/1 queue has been proved in[10].In this paper,we shall give the su？cient and necessary conditions of l-ergodicity,geometric ergodicity,and prove that they are neither uniformly polynomial ergodicity nor strong ergodicity.展开更多
Bandwidth,cutwidth,cyclic bandwidth,bandwidth sum and cyclic bandwidth sum are well-known indices about optimal labeling of graphs applied in VLSI design,network communications,and other areas involving the graph layo...Bandwidth,cutwidth,cyclic bandwidth,bandwidth sum and cyclic bandwidth sum are well-known indices about optimal labeling of graphs applied in VLSI design,network communications,and other areas involving the graph layout.To design the graphs with the given indices,we need to study the ergodicity.Let F be a set of graphs under consideration andφan integer-valued function defined on F,namely,φis an index,such as bandwidth and cutwidth.If there exists a graph G∈F such thatφ(G)=x for any integer x in the interval[a,b],where a and b are the minimum and maximum ofφon F,respectively,thenφis said to have ergodicity on F.Let Gnbe the set of simple connected graphs with order n and Tnthe set of trees with order n.In this paper,we investigate the ergodicity of bandwidth,cutwidth,cyclic bandwidth,the bandwidth sum and cyclic bandwidth sum on Tn and Gn.展开更多
In this paper, we investigate the flow of customers through queuing systems with randomly varying intensities. The analysis of the Kolmogorov-Chapman system of stationary equations for this model showed that it is not...In this paper, we investigate the flow of customers through queuing systems with randomly varying intensities. The analysis of the Kolmogorov-Chapman system of stationary equations for this model showed that it is not possible to construct a convenient symbolic solution. In this paper an attempt is made to circumvent this requirement by referring to the ergodicity theorems, which gives the conditions for the existence of the limit distribution in the service processes, but do not require knowledge of them.展开更多
We review the main aspects of the foundations of statistical mechanics. In particular we explain why many degrees of freedom are necessary, while chaos(in the sense of positive Lyapunov exponents) is only marginally r...We review the main aspects of the foundations of statistical mechanics. In particular we explain why many degrees of freedom are necessary, while chaos(in the sense of positive Lyapunov exponents) is only marginally relevant,for the emergence of statistical laws in macroscopic systems.展开更多
In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.
This paper investigates the ergodicity and weak convergence of transition probabilities for two-dimensional stochastic primitive equations driven by multiplicative noise.The existence of invariant measures is establis...This paper investigates the ergodicity and weak convergence of transition probabilities for two-dimensional stochastic primitive equations driven by multiplicative noise.The existence of invariant measures is established using the classical Krylov-Bogoliubov theory.The uniqueness of invariant measures and the weak convergence of transition probabilities are demonstrated through the application of the asymptotic coupling method and Foias-Prodi estimate.展开更多
This paper introduces the new class of periodic multivariate GARCH models in their periodic BEKK specification.Semi-polynomial Markov chains combined with algebraic geometry are used to obtain some properties like irr...This paper introduces the new class of periodic multivariate GARCH models in their periodic BEKK specification.Semi-polynomial Markov chains combined with algebraic geometry are used to obtain some properties like irreducibility.We impose weak conditions to obtain the strict periodic stationarity and the geometric ergodicity of the process,via the theory of positive linear operators on a cone:it is supposed that zero belongs to the support of the driving noise density which is absolutely continuous with respect to the Lebesgue measure and the spectral radius of a matrix built from the periodic coefficients of the model is smaller than one.展开更多
We establish the unique ergodicity of a fully discrete scheme for monotone SPDEs with polynomial growth drift and bounded diffusion coefficients driven by multiplicative white noise.The main ingredient of our method d...We establish the unique ergodicity of a fully discrete scheme for monotone SPDEs with polynomial growth drift and bounded diffusion coefficients driven by multiplicative white noise.The main ingredient of our method depends on the satisfaction of a Lyapunov condition followed by a uniform moments'estimate,combined with the regularity property for the full discretization.We transform the original stochastic equation into an equivalent random equation where the discrete stochastic convolutions are uniformly controlled to derive the desired uniform moments'estimate.Applying the main result to the stochastic Allen-Cahn equation driven by multiplicative white noise indicates that this full discretization is uniquely ergodic for any interface thickness.Numerical experiments validate our theoretical results.展开更多
Based on an explicit representation of moments of hitting times for single death processes, the criteria on ergodicity and strong ergodicity are obtained. These results can be applied for an extended class of branchin...Based on an explicit representation of moments of hitting times for single death processes, the criteria on ergodicity and strong ergodicity are obtained. These results can be applied for an extended class of branching processes. Meanwhile, some sufficient and necessary conditions for recurrence and exponential ergodicity as well as extinction probability for the processes are presented.展开更多
For an ergodic continuous-time Markov process with a particular state in its space,the authors provide the necessary and sufficient conditions for exponential and strong ergodicity in terms of the moments of the first...For an ergodic continuous-time Markov process with a particular state in its space,the authors provide the necessary and sufficient conditions for exponential and strong ergodicity in terms of the moments of the first hitting time on the state.An application to the queue length process of M/G/1 queue with multiple vacations is given.展开更多
In this paper,the Lipschitz ergodicity and generalized ergodicity are studied.Some criterions for a system to be Lipschitz ergodic or generalized ergodic are given.
This work focuses on a class of jump-diffusions with state-dependent switching. First, compared with the existing results in the literature, in our model, the characteristic measure is allowed to be a-finite. The exis...This work focuses on a class of jump-diffusions with state-dependent switching. First, compared with the existing results in the literature, in our model, the characteristic measure is allowed to be a-finite. The existence and uniqueness of the underlying process are obtained by representing the switching component as a stochastic integral with respect to a Poisson random measure and by using a successive approximation method. Then, the Feller property is proved by means of introducing auxiliary processes and by making use of Radon-Nikodym derivatives. Furthermore, the irreducibility and all compact sets being petite are demonstrated. Based on these results, the uniform ergodicity is established under a general Lyapunov condition. Finally, easily verifiable conditions for uniform ergodicity are established when the jump-diffusions are linearizable with respect to the variable x （the state variable corresponding to the jump-diffusion component） in a neighborhood of the infinity, and some examples are presented to illustrate the results.展开更多
We consider a modified Markov branching process incorporating with both state-independent immigration and instantaneous resurrection.The existence criterion of the process is firstly considered.We prove that if the su...We consider a modified Markov branching process incorporating with both state-independent immigration and instantaneous resurrection.The existence criterion of the process is firstly considered.We prove that if the sum of the resurrection rates is finite,then there does not exist any process.An existence criterion is then established when the sum of the resurrection rates is infinite.Some equivalent criteria,possessing the advantage of being easily checked,are obtained for the latter case.The uniqueness criterion for such process is also investigated.We prove that although there exist infinitely many of them,there always exists a unique honest process for a given q-matrix.This unique honest process is then constructed.The ergodicity property of this honest process is analysed in detail.We prove that this honest process is always ergodic and the explicit expression for the equilibrium distribution is established.展开更多
基金supported by National Natural Science Foundation of China(11001284)Natural Science Foundation Project of CQ CSTC(cstcjjA00003)Fundamental Research Funds for the Central Universities(CQDXWL2012008)
文摘In this paper, we define robust weak ergodicity and study the relation between robust weak ergodicity and stable ergodicity for conservative partially hyperbolic systems. We prove that a C^r（r 〉 1） conservative partially hyperbolic diffeomorphism is stably ergodic if it is robustly weakly ergodic and has positive （or negative） central exponents on a positive measure set. Furthermore, if the condition of robust weak ergodicity is replaced by weak ergodicity, then the diffeomophism is an almost stably ergodic system. Additionally, we show in dimension three, a C^r（r 〉 1） conservative partially hyperbolic diffeomorphism can be approximated by stably ergodic systems if it is robustly weakly ergodic and robustly has non-zero central exponents.
基金supported by the National Science Foundation of China(1067121290820302)the National Science Foundation of Hunan Province
文摘In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of（pt）t≥0 to equilibrium uniform on any bounded subset in H.
基金Supported by the National Natural Science Foundation of China(11571372,11771452)the Innovation Program of Central South University(10900-50601010)
文摘In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a quasi-birth-and-death process. As a byproduct of V-uniform ergodicity, we derive computable bounds on the exponential moments of the busy period.
基金supported by the National Natural Science Foundation of China (Grant Nos.61173183,60973152,and 60573172)the Superior University Doctor Subject Special Scientific Research Foundation of China (Grant No.20070141014)the Natural Science Foundation of Liaoning Province,China (Grant No.20082165)
文摘In this paper, we propose a new one-time one-key encryption algorithm based on the ergodicity of a skew tent chaotic map. We divide the chaotic trajectory into sub-intervals and map them to integers, and use this scheme to encrypt plaintext and obtain ciphertext. In this algorithm, the plaintext information in the key is used, so different plaintexts or different total numbers of plaintext letters will encrypt different ciphertexts. Simulation results show that the performance and the security of the proposed encryption algorithm can encrypt plaintext effectively and resist various typical attacks.
基金supported by National Natural Science Foundation of China under Grant No.10774150
文摘At low temperatures the configurational phase space of a macroscopic complex system （e.g., a spin-glass） of N - 10^23 interacting particles may split into an exponential number Ωs - exp（const × N） of ergodic sub-spaces （thermodynamic states）. It is usually assumed that the equilibrium collective behavior of such a system is determined by its ground thermodynamic states of the minimal free-energy density, and that the equilibrium free energies follow the distribution of exponentied decay. But actually for some complex systems, the equilibrium free-energy values may follow a Gaussian distribution within an intermediate temperature range, and consequently their equilibrium properties are contributed by excited thermodynamic states. Based on this analysis, the re-weighting parameter y in the cavity approach of spin-glasses is easily understood. Depending on the free-energy distribution, the optimal y can either be equal to or be strictly less than the inverse temperature β.
文摘Let X be a compact metric space and C（X） be the space of all continuous functions on X. In this article, the authors consider the Markov operator T ： C（X）N C（X）N defined by for any f = （f1,f2,… ,fN）, where （pij） is a N x N transition probability matrix and {wij } is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T＊-invariant measures where T＊ is the adjoint operator of T.
文摘The finite data estimates of the complex fourth-order moments of a signal consisting of random harmonics are analyzed. Conditions for the fourth-order stationarity and ergodicity are obtained. Explicit formulas for the estimation error and its variance, as well as their limiting large sample values are derived. Finally, a special case relevant to cubic phase coupling is considered, and these results are stated for this case, the variance is shown to comprise an ergodic and a nonergodic part.
基金Supported by the Chinese Universities Scientific Fund(BUPT2009RC0707,BUPT2011RC0703)
文摘The IP P＋M/M/c queueing system has been extensively used in the modern communication system.The existence and uniqueness of stationary distribution of the queue length L（t）for IP P＋M/M/1 queue has been proved in[10].In this paper,we shall give the su？cient and necessary conditions of l-ergodicity,geometric ergodicity,and prove that they are neither uniformly polynomial ergodicity nor strong ergodicity.
基金Supported by Science and Technology Program of Guangzhou(Grant No.202002030183)Natural Science Foundation of Guangdong(Grant No.2021A1515012045)+1 种基金National Natural Science Foundation of China(Grant No.12161073)Natural Science Foundation of Qinghai(Grant No.2020-ZJ-924)。
文摘Bandwidth,cutwidth,cyclic bandwidth,bandwidth sum and cyclic bandwidth sum are well-known indices about optimal labeling of graphs applied in VLSI design,network communications,and other areas involving the graph layout.To design the graphs with the given indices,we need to study the ergodicity.Let F be a set of graphs under consideration andφan integer-valued function defined on F,namely,φis an index,such as bandwidth and cutwidth.If there exists a graph G∈F such thatφ(G)=x for any integer x in the interval[a,b],where a and b are the minimum and maximum ofφon F,respectively,thenφis said to have ergodicity on F.Let Gnbe the set of simple connected graphs with order n and Tnthe set of trees with order n.In this paper,we investigate the ergodicity of bandwidth,cutwidth,cyclic bandwidth,the bandwidth sum and cyclic bandwidth sum on Tn and Gn.
文摘In this paper, we investigate the flow of customers through queuing systems with randomly varying intensities. The analysis of the Kolmogorov-Chapman system of stationary equations for this model showed that it is not possible to construct a convenient symbolic solution. In this paper an attempt is made to circumvent this requirement by referring to the ergodicity theorems, which gives the conditions for the existence of the limit distribution in the service processes, but do not require knowledge of them.
文摘We review the main aspects of the foundations of statistical mechanics. In particular we explain why many degrees of freedom are necessary, while chaos(in the sense of positive Lyapunov exponents) is only marginally relevant,for the emergence of statistical laws in macroscopic systems.
文摘In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.
基金supported in part by the NSFC(12171084,12326367)the Jiangsu Provincial Scientific Research Center of Applied Mathematics(BK20233002)the fundamental Research Funds for the Central Universities(RF1028623037)。
文摘This paper investigates the ergodicity and weak convergence of transition probabilities for two-dimensional stochastic primitive equations driven by multiplicative noise.The existence of invariant measures is established using the classical Krylov-Bogoliubov theory.The uniqueness of invariant measures and the weak convergence of transition probabilities are demonstrated through the application of the asymptotic coupling method and Foias-Prodi estimate.
基金the support of the University of Science and Technology Houari Boumediene (USTHB) and the Ministry of Higher Education and Scientific Research, Algiers, Algeria for the PNR 25/08the support of the University of Médéa, Algeria
文摘This paper introduces the new class of periodic multivariate GARCH models in their periodic BEKK specification.Semi-polynomial Markov chains combined with algebraic geometry are used to obtain some properties like irreducibility.We impose weak conditions to obtain the strict periodic stationarity and the geometric ergodicity of the process,via the theory of positive linear operators on a cone:it is supposed that zero belongs to the support of the driving noise density which is absolutely continuous with respect to the Lebesgue measure and the spectral radius of a matrix built from the periodic coefficients of the model is smaller than one.
基金supported by the National Natural Science Foundation of China(No.12101296)by the Basic and Applied Basic Research Foundation of Guang dong Province(No.2024A1515012348)by the Shenzhen Basic Research Special Project(Natural Science Foundation)Basic Research(General Project)(Nos.JCYJ20220530112814033,JCYJ20240813094919026).
文摘We establish the unique ergodicity of a fully discrete scheme for monotone SPDEs with polynomial growth drift and bounded diffusion coefficients driven by multiplicative white noise.The main ingredient of our method depends on the satisfaction of a Lyapunov condition followed by a uniform moments'estimate,combined with the regularity property for the full discretization.We transform the original stochastic equation into an equivalent random equation where the discrete stochastic convolutions are uniformly controlled to derive the desired uniform moments'estimate.Applying the main result to the stochastic Allen-Cahn equation driven by multiplicative white noise indicates that this full discretization is uniquely ergodic for any interface thickness.Numerical experiments validate our theoretical results.
文摘Based on an explicit representation of moments of hitting times for single death processes, the criteria on ergodicity and strong ergodicity are obtained. These results can be applied for an extended class of branching processes. Meanwhile, some sufficient and necessary conditions for recurrence and exponential ergodicity as well as extinction probability for the processes are presented.
基金the National Natural Science Foundation of China(No.10671212)the Research Fund for the Doctoral Program of Higher Education(No.20050533036).
文摘For an ergodic continuous-time Markov process with a particular state in its space,the authors provide the necessary and sufficient conditions for exponential and strong ergodicity in terms of the moments of the first hitting time on the state.An application to the queue length process of M/G/1 queue with multiple vacations is given.
基金supported by National Natural Science Foundation of China (Grant No.11071238)the Key Lab of Random Complex Structures and Data Science,CAS and NCMIS Aca demy of Mathematics and Systems Science,Chinese Academy of Sciences
文摘In this paper,the Lipschitz ergodicity and generalized ergodicity are studied.Some criterions for a system to be Lipschitz ergodic or generalized ergodic are given.
基金supported in part by National Natural Science Foundation of China(Grant No. 11171024)supported in part by National Natural Science Foundation of China (Grant No.70871055)supported in part by National Science Foundationof US (Grant No. DMS-0907753)
文摘This work focuses on a class of jump-diffusions with state-dependent switching. First, compared with the existing results in the literature, in our model, the characteristic measure is allowed to be a-finite. The existence and uniqueness of the underlying process are obtained by representing the switching component as a stochastic integral with respect to a Poisson random measure and by using a successive approximation method. Then, the Feller property is proved by means of introducing auxiliary processes and by making use of Radon-Nikodym derivatives. Furthermore, the irreducibility and all compact sets being petite are demonstrated. Based on these results, the uniform ergodicity is established under a general Lyapunov condition. Finally, easily verifiable conditions for uniform ergodicity are established when the jump-diffusions are linearizable with respect to the variable x （the state variable corresponding to the jump-diffusion component） in a neighborhood of the infinity, and some examples are presented to illustrate the results.
基金partially supported by the National Natural Science Foundation of China (Grant No. 10771216)Research Grants Council of Hong Kong (Grant No. HKU 7010/06P)Project-sponsored by SRF for ROCS,SEM
文摘We consider a modified Markov branching process incorporating with both state-independent immigration and instantaneous resurrection.The existence criterion of the process is firstly considered.We prove that if the sum of the resurrection rates is finite,then there does not exist any process.An existence criterion is then established when the sum of the resurrection rates is infinite.Some equivalent criteria,possessing the advantage of being easily checked,are obtained for the latter case.The uniqueness criterion for such process is also investigated.We prove that although there exist infinitely many of them,there always exists a unique honest process for a given q-matrix.This unique honest process is then constructed.The ergodicity property of this honest process is analysed in detail.We prove that this honest process is always ergodic and the explicit expression for the equilibrium distribution is established.
