The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average d...The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems,assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.展开更多
In this article, we construct an exponential martingale for the compound Poisson process with latent variable. With the help of this exponential martingale, we provide an asymptotic behavior of the coherent entropic r...In this article, we construct an exponential martingale for the compound Poisson process with latent variable. With the help of this exponential martingale, we provide an asymptotic behavior of the coherent entropic risk measure for the compound Poisson process and a deviation inequality for the ruin probability of the partly shifted risk process.展开更多
In this paper, we introduce the definition of Γ-Fisher entropy. For the stochastic differential equation in Rd and the unique invariant probability measure μ, we obtain the exponential convergence of Γ-Fisher entro...In this paper, we introduce the definition of Γ-Fisher entropy. For the stochastic differential equation in Rd and the unique invariant probability measure μ, we obtain the exponential convergence of Γ-Fisher entropy with respect to μ under some condition about Γ and the drift b. Moreover, we revisit the exponential convergence of the usual Fisher entropy under the Bakry Emery condition.展开更多
A modified exponentially weighted moving average (EWMA) scheme is one of the quality control charts suchthat this control chart can quickly detect a small shift. The average run length (ARL) is frequently used for the...A modified exponentially weighted moving average (EWMA) scheme is one of the quality control charts suchthat this control chart can quickly detect a small shift. The average run length (ARL) is frequently used for theperformance evaluation on control charts. This paper proposes the explicit formula for evaluating the average runlength on a two-sided modified exponentially weighted moving average chart under the observations of a first-orderautoregressive process, referred to as AR(1) process, with an exponential white noise. The performance comparisonof the explicit formula and the numerical integral technique is carried out using the absolute relative change forchecking the correct formula and the CPU time for testing speed of calculation. The results show that the ARL ofthe explicit formula and the numerical integral equation method are hardly different, but this explicit formula ismuch faster for calculating the ARL and offered accurate values. Furthermore, the cumulative sum, the classicalEWMA and the modified EWMA control charts are compared and the results show that the latter is better for smalland intermediate shift sizes. In addition, the explicit formula is successfully applied to real-world data in the healthfield as COVID-19 data in Thailand and Singapore.展开更多
We give an extension of Delyon's inequality for locally square integrable martingales.The result is very useful for establishing self-normalized exponential inequality for martingales.An application to linear regr...We give an extension of Delyon's inequality for locally square integrable martingales.The result is very useful for establishing self-normalized exponential inequality for martingales.An application to linear regressions is discussed.展开更多
Blue photoluminescence is observed in aged porous silicon samples anodized under Ar^(+)488 nm laser illumination.No samples have been undergone any heating treatment process.Both nanosecond and microsecond decay of bl...Blue photoluminescence is observed in aged porous silicon samples anodized under Ar^(+)488 nm laser illumination.No samples have been undergone any heating treatment process.Both nanosecond and microsecond decay of blue photoluminescence have been measured.Samples show a good monoexponential microsecond decay with lifetimes of about 5.3μs.Photoluminescence excitation spectra of blue and red Photoluminescence indicate there is a large Stokes shift(about 800-900meV)in the excitation spectra of red photoluminescence while no this marked Stokes shift in that of blue photoluminescence.The possible origin of the photoluminescence is discussed based on the experimental results.展开更多
In this paper, we consider a hyper-exponential jump-diffusion model with a constant dividend barrier. Explicit solutions for the Laplace transform of the ruin time, and the Gerber- Shiu function are obtained via marti...In this paper, we consider a hyper-exponential jump-diffusion model with a constant dividend barrier. Explicit solutions for the Laplace transform of the ruin time, and the Gerber- Shiu function are obtained via martingale stopping.展开更多
Remaining Useful Life(RUL)is one of the most important indicators to detect a component failure.RUL can be predicted by historical data by adopting a model-based method.The stochastic process models have become the mo...Remaining Useful Life(RUL)is one of the most important indicators to detect a component failure.RUL can be predicted by historical data by adopting a model-based method.The stochastic process models have become the most popular way to model degradation data for high-quality products,such as the Wiener process,gamma process and inverse Gaussian process.However,this leads to poor reliability assessment if the model is misspecified.Application of the Tweedie exponential dispersion(TED)process,including the above-mentioned classical stochastic processes as special cases,transforms the model selection problem into a parameter estimation problem dexterously.In this paper,we propose a TED process with random drifts for degradation data and a TeD process with random drifts and covariates for accelerated degradation data.A hierarchical Bayesian method is adopted to estimate the parameters of the proposed models.We also derive the failure-time distribution and the remaining useful life distribution for the proposed models.The simulation study shows that the proposed model outperforms the wrongly specified models.Two illustrative examples demonstrate the performance of the proposed TED process with random drifts and the TED process with random drifts and covariates.展开更多
Let Q be the Q-matrix of an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augme...Let Q be the Q-matrix of an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augmentations of Q converge in total variation to the stationary distribution of the process. Two conditions guaranteeing such convergence include exponential ergodicity and stochastic monotonicity of the process. The same also holds for processes dominated by a stochastically monotone Markov process. In addition, we shall show that finite perturbations of stochastically monotone processes may be viewed as being dominated by a stochastically monotone process, thus extending the scope of these results to a larger class of processes. Consequently, the augmentation method provides an attractive, intuitive method for approximating the stationary distributions of a large class of Markov processes on countably infinite state spaces from a finite amount of known information.展开更多
The homogenous Poisson process is often used to describe the event arrivals. Such Poisson process has been applied in various areas. This study focuses on the arrival pattern of storm water overflows. A set of overflo...The homogenous Poisson process is often used to describe the event arrivals. Such Poisson process has been applied in various areas. This study focuses on the arrival pattern of storm water overflows. A set of overflow data was obtained from the storm water pipeline of a municipality. The aim is to verify the overflow arrival pattern and check whether the Poisson process can be applied. The adopted method is the analysis over the inter-arrival times. The exponential distribution test is conducted on the annual data set as well as the entire data set. The results show that all data sets follow the exponential distribution. With the verification of Poisson process, specific examples are also given to show how the Poisson process properties can be used in the management of storm water pipeline management. For other data that are featured with various heterogeneities, the homogenous Poisson process might not be able to be verified and used. Under such circumstances, non-homogenous survival model can be used to simulate the arrival process.展开更多
In this article, we consider the long time behavior of the solutions to stochastic wave equations driven by a non-Gaussian Lévy process. We shall prove that under some appropriate conditions, the exponential stab...In this article, we consider the long time behavior of the solutions to stochastic wave equations driven by a non-Gaussian Lévy process. We shall prove that under some appropriate conditions, the exponential stability of the solutions holds. Finally, we give two examples to illustrate our results.展开更多
Consistent high-quality and defect-free production is the demand of the day. The product recall not only increases engineering and manufacturing cost but also affects the quality and the reliability of the product in ...Consistent high-quality and defect-free production is the demand of the day. The product recall not only increases engineering and manufacturing cost but also affects the quality and the reliability of the product in the eye of users. The monitoring and improvement of a manufacturing process are the strength of statistical process control. In this article we propose a process monitoring memory-based scheme for continuous data under the assumption of normality to detect small non-random shift patterns in any manufacturing or service process.The control limits for the proposed scheme are constructed. The in-control and out-of-control average run length(AVL) expressions have been derived for the performance evaluation of the proposed scheme. Robustness to non-normality has been tested after simulation study of the run length distribution of the proposed scheme, and the comparisons with Shewhart and exponentially weighted moving average(EWMA) schemes are presented for various gamma and t-distributions. The proposed scheme is effective and attractive as it has one design parameter which differentiates it from the traditional schemes. Finally, some suggestions and recommendations are made for the future work.展开更多
A novel nonlinear combination process monitoring method was proposed based on techniques with memo- ry effect （multivariate exponentially weighted moving average （MEWMA）） and kernel independent component analysis ...A novel nonlinear combination process monitoring method was proposed based on techniques with memo- ry effect （multivariate exponentially weighted moving average （MEWMA）） and kernel independent component analysis （KICA）. The method was developed for dealing with nonlinear issues and detecting small or moderate drifts in one or more process variables with autocorrelation. MEWMA charts use additional information from the past history of the process for keeping the memory effect of the process behavior trend. KICA is a recently devel- oped statistical technique for revealing hidden, nonlinear statistically independent factors that underlie sets of mea- surements and it is a two-phase algorithm., whitened kernel principal component analysis （KPCA） plus indepen- dent component analysis （ICA）. The application to the fluid catalytic cracking unit （FCCU） simulated process in- dicates that the proposed combined method based on MEWMA and KICA can effectively capture the nonlinear rela- tionship and detect small drifts in process variables. Its performance significantly outperforms monitoring method based on ICA, MEWMA-ICA and KICA, especially for lonu-term performance deterioration.展开更多
A model for dynamic frictionless contact between a viscoelastic body and foundation is considered.The viscoelastic constitutive law is assumed to be nonlinear and the contact is modelled with the normal compliance con...A model for dynamic frictionless contact between a viscoelastic body and foundation is considered.The viscoelastic constitutive law is assumed to be nonlinear and the contact is modelled with the normal compliance condition.We obtain the well-posedness using nonlinear semigroup theory arguments.Moreover,the exponential stability result of the solution is shown by using the energy method to produce a suitable Lyapunov function.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
基金the National Natural Science Foundation of China (60674027, 60574007)Doctoral Foundation of Education Ministry of China (20050446001).
文摘The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems,assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.
基金Supported by National Natural Science Foundation of China(11301461)Natural Science Foundation of Jiangsu Province(BK20130435)University Natural Science Foundation of Jiangsu Province(13KJB110031)
文摘In this article, we construct an exponential martingale for the compound Poisson process with latent variable. With the help of this exponential martingale, we provide an asymptotic behavior of the coherent entropic risk measure for the compound Poisson process and a deviation inequality for the ruin probability of the partly shifted risk process.
基金Supported by the National Natural Science Foundation of China (11001208)the Fundamental Research Funds for the Central Universities
文摘In this paper, we introduce the definition of Γ-Fisher entropy. For the stochastic differential equation in Rd and the unique invariant probability measure μ, we obtain the exponential convergence of Γ-Fisher entropy with respect to μ under some condition about Γ and the drift b. Moreover, we revisit the exponential convergence of the usual Fisher entropy under the Bakry Emery condition.
基金The research was supported by King Mongkut’s University of Technology North Bangkok Contract No.KMUTNB-62-KNOW-018.
文摘A modified exponentially weighted moving average (EWMA) scheme is one of the quality control charts suchthat this control chart can quickly detect a small shift. The average run length (ARL) is frequently used for theperformance evaluation on control charts. This paper proposes the explicit formula for evaluating the average runlength on a two-sided modified exponentially weighted moving average chart under the observations of a first-orderautoregressive process, referred to as AR(1) process, with an exponential white noise. The performance comparisonof the explicit formula and the numerical integral technique is carried out using the absolute relative change forchecking the correct formula and the CPU time for testing speed of calculation. The results show that the ARL ofthe explicit formula and the numerical integral equation method are hardly different, but this explicit formula ismuch faster for calculating the ARL and offered accurate values. Furthermore, the cumulative sum, the classicalEWMA and the modified EWMA control charts are compared and the results show that the latter is better for smalland intermediate shift sizes. In addition, the explicit formula is successfully applied to real-world data in the healthfield as COVID-19 data in Thailand and Singapore.
文摘We give an extension of Delyon's inequality for locally square integrable martingales.The result is very useful for establishing self-normalized exponential inequality for martingales.An application to linear regressions is discussed.
基金Supported by the National Natural Science Foundation of China under Grant No.59372108the Laboratory of Excited State Processes,Changchun Institute of Physics,Chinese Academy of Sciences。
文摘Blue photoluminescence is observed in aged porous silicon samples anodized under Ar^(+)488 nm laser illumination.No samples have been undergone any heating treatment process.Both nanosecond and microsecond decay of blue photoluminescence have been measured.Samples show a good monoexponential microsecond decay with lifetimes of about 5.3μs.Photoluminescence excitation spectra of blue and red Photoluminescence indicate there is a large Stokes shift(about 800-900meV)in the excitation spectra of red photoluminescence while no this marked Stokes shift in that of blue photoluminescence.The possible origin of the photoluminescence is discussed based on the experimental results.
基金Supported by the Natural Science Foundation of Jiangsu Province(BK20130260)the National Natural Science Foundation of China(11301369)the Postdoctoral Science Foundation of China(2013M540371)
文摘In this paper, we consider a hyper-exponential jump-diffusion model with a constant dividend barrier. Explicit solutions for the Laplace transform of the ruin time, and the Gerber- Shiu function are obtained via martingale stopping.
基金supported by the National Natural Science Foundation of China[grant number 12001266]Natural Science Foundation of Jiangsu Province of China[grant number BK20180813]supported by the National Natural Science Foundation of China[grant number 12271168,12531013]and the 111 Project of China[grant number B14019].
文摘Remaining Useful Life(RUL)is one of the most important indicators to detect a component failure.RUL can be predicted by historical data by adopting a model-based method.The stochastic process models have become the most popular way to model degradation data for high-quality products,such as the Wiener process,gamma process and inverse Gaussian process.However,this leads to poor reliability assessment if the model is misspecified.Application of the Tweedie exponential dispersion(TED)process,including the above-mentioned classical stochastic processes as special cases,transforms the model selection problem into a parameter estimation problem dexterously.In this paper,we propose a TED process with random drifts for degradation data and a TeD process with random drifts and covariates for accelerated degradation data.A hierarchical Bayesian method is adopted to estimate the parameters of the proposed models.We also derive the failure-time distribution and the remaining useful life distribution for the proposed models.The simulation study shows that the proposed model outperforms the wrongly specified models.Two illustrative examples demonstrate the performance of the proposed TED process with random drifts and the TED process with random drifts and covariates.
文摘Let Q be the Q-matrix of an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augmentations of Q converge in total variation to the stationary distribution of the process. Two conditions guaranteeing such convergence include exponential ergodicity and stochastic monotonicity of the process. The same also holds for processes dominated by a stochastically monotone Markov process. In addition, we shall show that finite perturbations of stochastically monotone processes may be viewed as being dominated by a stochastically monotone process, thus extending the scope of these results to a larger class of processes. Consequently, the augmentation method provides an attractive, intuitive method for approximating the stationary distributions of a large class of Markov processes on countably infinite state spaces from a finite amount of known information.
文摘The homogenous Poisson process is often used to describe the event arrivals. Such Poisson process has been applied in various areas. This study focuses on the arrival pattern of storm water overflows. A set of overflow data was obtained from the storm water pipeline of a municipality. The aim is to verify the overflow arrival pattern and check whether the Poisson process can be applied. The adopted method is the analysis over the inter-arrival times. The exponential distribution test is conducted on the annual data set as well as the entire data set. The results show that all data sets follow the exponential distribution. With the verification of Poisson process, specific examples are also given to show how the Poisson process properties can be used in the management of storm water pipeline management. For other data that are featured with various heterogeneities, the homogenous Poisson process might not be able to be verified and used. Under such circumstances, non-homogenous survival model can be used to simulate the arrival process.
基金supported by National Natural Science Foundation of China(11571190)the Fundamental Research Funds for the Central Universities+3 种基金supported by the China Scholarship Council(201807315008)National Natural Science Foundation of China(11501565)the Youth Project of Humanities and Social Sciences of Ministry of Education(19YJCZH251)supported by National Natural Science Foundation of China(11701084 and 11671084)
文摘In this article, we consider the long time behavior of the solutions to stochastic wave equations driven by a non-Gaussian Lévy process. We shall prove that under some appropriate conditions, the exponential stability of the solutions holds. Finally, we give two examples to illustrate our results.
文摘Consistent high-quality and defect-free production is the demand of the day. The product recall not only increases engineering and manufacturing cost but also affects the quality and the reliability of the product in the eye of users. The monitoring and improvement of a manufacturing process are the strength of statistical process control. In this article we propose a process monitoring memory-based scheme for continuous data under the assumption of normality to detect small non-random shift patterns in any manufacturing or service process.The control limits for the proposed scheme are constructed. The in-control and out-of-control average run length(AVL) expressions have been derived for the performance evaluation of the proposed scheme. Robustness to non-normality has been tested after simulation study of the run length distribution of the proposed scheme, and the comparisons with Shewhart and exponentially weighted moving average(EWMA) schemes are presented for various gamma and t-distributions. The proposed scheme is effective and attractive as it has one design parameter which differentiates it from the traditional schemes. Finally, some suggestions and recommendations are made for the future work.
基金The National Natural Science Foundation ofChina(No60504033)
文摘A novel nonlinear combination process monitoring method was proposed based on techniques with memo- ry effect （multivariate exponentially weighted moving average （MEWMA）） and kernel independent component analysis （KICA）. The method was developed for dealing with nonlinear issues and detecting small or moderate drifts in one or more process variables with autocorrelation. MEWMA charts use additional information from the past history of the process for keeping the memory effect of the process behavior trend. KICA is a recently devel- oped statistical technique for revealing hidden, nonlinear statistically independent factors that underlie sets of mea- surements and it is a two-phase algorithm., whitened kernel principal component analysis （KPCA） plus indepen- dent component analysis （ICA）. The application to the fluid catalytic cracking unit （FCCU） simulated process in- dicates that the proposed combined method based on MEWMA and KICA can effectively capture the nonlinear rela- tionship and detect small drifts in process variables. Its performance significantly outperforms monitoring method based on ICA, MEWMA-ICA and KICA, especially for lonu-term performance deterioration.
文摘A model for dynamic frictionless contact between a viscoelastic body and foundation is considered.The viscoelastic constitutive law is assumed to be nonlinear and the contact is modelled with the normal compliance condition.We obtain the well-posedness using nonlinear semigroup theory arguments.Moreover,the exponential stability result of the solution is shown by using the energy method to produce a suitable Lyapunov function.
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.
