Let Ls be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of Ls is obtained, and the sufficient and necessary condition for E^x（L^κB） 〈∞ is pr...Let Ls be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of Ls is obtained, and the sufficient and necessary condition for E^x（L^κB） 〈∞ is proved.展开更多
In this paper,we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are generated by stationary weakly and strongly dependent Gaussian sequences.I...In this paper,we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are generated by stationary weakly and strongly dependent Gaussian sequences.It is shown that the first crossing point and the last exit time are asymptotically independent and dependent for weakly and strongly dependent cases,respectively.The asymptotic relations between the first crossing point and the last exit time for stationary weakly and strongly dependent Gaussian sequences are also obtained.展开更多
This paper considers a Manpower system where “exits” of employed personnel produce some wastage or loss. This system monitors these wastages over the sequence of exit epochs {t0 = 0 and tk;k = 1, 2,…} that form a r...This paper considers a Manpower system where “exits” of employed personnel produce some wastage or loss. This system monitors these wastages over the sequence of exit epochs {t0 = 0 and tk;k = 1, 2,…} that form a recurrent process and admit recruitment when the cumulative loss of man hours crosses a threshold level Y, which is also called the breakdown level. It is assumed that the inter-exit times Tk = tk-1 - tk, k = 1, 2,… are independent and identically distributed random variables with a common cumulative distribution function (CDF) B(t) = P(Tk t) which has a tail 1 – B(t) behaving like t-v with 1 v as t → ∞. The amounts {Xk} of wastages incurred during these inter-exit times {Tk} are independent and identically distributed random variables with CDF P(Xk X) = G(x) and Y is distributed, independently of {Xk} and {tk}, as an exponentiated exponential law with CDF H(y) = P(Y y) = (1 - e-λy)n. The mean waiting time to break down of the system has been obtained assuming B(t) to be heavy tailed and as well as light tailed. For the exponential case of G(x), a comparative study has also been made between heavy tailed mean waiting time to break down and light tailed mean waiting time to break down values. The recruitment policy operating under the heavy tailed case is shown to be more economical in all types of manpower systems.展开更多
In this paper, we study infinite-period mean-variance formulations for portfolio selections with an uncertain exit time. We employ the convergence control method together with the dynamic programming algorithm to deri...In this paper, we study infinite-period mean-variance formulations for portfolio selections with an uncertain exit time. We employ the convergence control method together with the dynamic programming algorithm to derive analytical expressions for the optimal portfolio policy and the mean-variance efficient frontier under certain conditions. We illustrate these results by an numerical example.展开更多
Given a compact symmetric space, M, we obtain the mean exit time function from a principal orbit, for a Brownian particle starting and moving in a generalized ball whose boundary is the principal orbit. We also obtain...Given a compact symmetric space, M, we obtain the mean exit time function from a principal orbit, for a Brownian particle starting and moving in a generalized ball whose boundary is the principal orbit. We also obtain the mean exit time flmction of a tube of radius r around special totally geodesic submanifolds P of M. Finally we give a comparison result for the mean exit time function of tubes around submanifolds in Riemannian manifolds, using these totally geodesic submanifolds in compact symmetric spaces as a model.展开更多
We obtain upper and lower bounds of the exit times from balls of a jump-type symmetric Markov process. The proofs are delivered separately. The upper bounds are obtained by using the Levy system corresponding to the p...We obtain upper and lower bounds of the exit times from balls of a jump-type symmetric Markov process. The proofs are delivered separately. The upper bounds are obtained by using the Levy system corresponding to the process, while the precise expression of the （L^2-）generator of the Dirichlet form associated with the process is used to obtain the lower bounds.展开更多
Let {Xn} be a Markov chain with transition probability pij =： aj-（i-1）＋,i,j ≥ 0, where aj=0 providedj 〈 0, a0 〉 0, a0＋a1〈 1 and ∑∞n=0 an= 1. Let μ∑∞n=1nan. It is known that {Xn} is positive recurrent wh...Let {Xn} be a Markov chain with transition probability pij =： aj-（i-1）＋,i,j ≥ 0, where aj=0 providedj 〈 0, a0 〉 0, a0＋a1〈 1 and ∑∞n=0 an= 1. Let μ∑∞n=1nan. It is known that {Xn} is positive recurrent when μ 〈 1; is null recurrent when μ= 1; and is transient when μ 〉 1. In this paper, the integrability of the first returning time and the last exit time are discussed. Keywords Geom/G/1 queuing model, first returning time, last exit time, Markov chain展开更多
0 .Introduction The mathematical eqnivalenoe of Brownian切otion and olaosioal poten七ialtheory has great imPulsed the study of Potentials of Markov Prooesse
Space time trellis coding （STTC） techniques have been proposed to achieve both diversity and coding gains in multiple input multiple output （MIMO） fading channels. But with more transmit antennas STTCs suffer from...Space time trellis coding （STTC） techniques have been proposed to achieve both diversity and coding gains in multiple input multiple output （MIMO） fading channels. But with more transmit antennas STTCs suffer from the design dificulty and complexity increasing. This paper proposes a scheme, named parallel concatenated space time trellis codes （PC-STTC）, to achieve the tradeoff between the performances and complexity of STTCs for a large number of transmit antennas. Simulation results and complexity comparison are provided to demonstrate the performance and superiority of the proposed scheme over conventional schemes in fast fading channels in low signal-to-noise ratio （SNR） regions. And an EXIT （extrinsic information transform） chart is given to analyze the iterative convergence of the proposed scheme. It shows that PC-STTC has better iterative convergence in low SNR regions.展开更多
The motion of a lazy Pearson walker is studied with different probability (p) of jump in two and three dimensions. The probability of exit ( ) from a zone of radius is studied as a function of with d...The motion of a lazy Pearson walker is studied with different probability (p) of jump in two and three dimensions. The probability of exit ( ) from a zone of radius is studied as a function of with different values of jump probability p. The exit probability is found to scale as , which is obtained by method of data collapse. The first passage time ( ) i.e., the time required for first exit from a zone is studied. The probability distribution of first passage time was studied for different values of jump probability (p). The probability distribution of first passage time was found to scale as . Where, F and G are two scaling functions and a, b, g and d are some exponents. In both the dimensions, it is found that, , , and .展开更多
Suppose X is a super-α-stable process in R^d, （0 〈 α〈 2）, whose branching rate function is dr, and branching mechanism is of the form ψ（z） = z^1＋β （0 〈0 〈β ≤1）. Let Xγ and Yγ denote the exit measur...Suppose X is a super-α-stable process in R^d, （0 〈 α〈 2）, whose branching rate function is dr, and branching mechanism is of the form ψ（z） = z^1＋β （0 〈0 〈β ≤1）. Let Xγ and Yγ denote the exit measure and the total weighted occupation time measure of X in a bounded smooth domain D, respectively. The absolute continuities of Xγ and Yγ are discussed.展开更多
In this paper, we consider the two-sided first exit problem for jump diffusion processes having jumps with rational Laplace transforms. We investigate the probabilistic property of conditional memorylessness, and driv...In this paper, we consider the two-sided first exit problem for jump diffusion processes having jumps with rational Laplace transforms. We investigate the probabilistic property of conditional memorylessness, and drive the joint distribution of the first exit time from an interval and the overshoot over the boundary at the exit time.展开更多
Residence time in a flow measurement of radioactivity is the time spent by a pre-determined quantity of radioactive sample in the flow cell. In a recent report of the measurement of indoor radon by passive diffusion i...Residence time in a flow measurement of radioactivity is the time spent by a pre-determined quantity of radioactive sample in the flow cell. In a recent report of the measurement of indoor radon by passive diffusion in an open volume (i.e. no flow cell or control volume), the concept of residence time was generalized to apply to measurement conditions with random, rather than directed, flow. The generalization, leading to a quantity Δtr, involved use of a) a phenomenological alpha-particle range function to calculate the effective detection volume, and b) a phenomenological description of diffusion by Fick’s law to determine the effective flow velocity. This paper examines the residence time in passive diffusion from the micro-statistical perspective of single-particle continuous Brownian motion. The statistical quantity “mean residence time” Tr is derived from the Green’s function for unbiased single-particle diffusion and is shown to be consistent with Δtr. The finite statistical lifetime of the randomly moving radioactive atom plays an essential part. For stable particles, Tr is of infinite duration, whereas for an unstable particle (such as 222Rn), with diffusivity D and decay rate λ, Tr is approximately the effective size of the detection region divided by the characteristic diffusion velocity . Comparison of the mean residence time with the time of first passage (or exit time) in the theory of stochastic processes shows the conditions under which the two measures of time are equivalent and helps elucidate the connection between the phenomenological and statistical descriptions of radon diffusion.展开更多
基金Research supported in part by Tianyuan Fund ofr Mathematics of NSFC (10526021)A Grant from Ministry of Education
文摘Let Ls be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of Ls is obtained, and the sufficient and necessary condition for E^x（L^κB） 〈∞ is proved.
基金Supported by the National Natural Science Foundation of China(11501250)Zhejiang Provincial Natural Science Foundation of China(LY18A010020)Innovation of Jiaxing City:a program to support the talented persons。
文摘In this paper,we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are generated by stationary weakly and strongly dependent Gaussian sequences.It is shown that the first crossing point and the last exit time are asymptotically independent and dependent for weakly and strongly dependent cases,respectively.The asymptotic relations between the first crossing point and the last exit time for stationary weakly and strongly dependent Gaussian sequences are also obtained.
文摘This paper considers a Manpower system where “exits” of employed personnel produce some wastage or loss. This system monitors these wastages over the sequence of exit epochs {t0 = 0 and tk;k = 1, 2,…} that form a recurrent process and admit recruitment when the cumulative loss of man hours crosses a threshold level Y, which is also called the breakdown level. It is assumed that the inter-exit times Tk = tk-1 - tk, k = 1, 2,… are independent and identically distributed random variables with a common cumulative distribution function (CDF) B(t) = P(Tk t) which has a tail 1 – B(t) behaving like t-v with 1 v as t → ∞. The amounts {Xk} of wastages incurred during these inter-exit times {Tk} are independent and identically distributed random variables with CDF P(Xk X) = G(x) and Y is distributed, independently of {Xk} and {tk}, as an exponentiated exponential law with CDF H(y) = P(Y y) = (1 - e-λy)n. The mean waiting time to break down of the system has been obtained assuming B(t) to be heavy tailed and as well as light tailed. For the exponential case of G(x), a comparative study has also been made between heavy tailed mean waiting time to break down and light tailed mean waiting time to break down values. The recruitment policy operating under the heavy tailed case is shown to be more economical in all types of manpower systems.
基金Supported by the Natural Science Foundation of China(No.71071071,11101205)Ministry of Education Social Science Research Fund Planning Project,China Postdoctoral Science Foundation(No.200902507,20080431079)+1 种基金Nanjing University of Finance&Economics Science Research Foundation(2012Y1204)the Natural Sciences and Engineering Research Council of Canada(NSERC)
文摘In this paper, we study infinite-period mean-variance formulations for portfolio selections with an uncertain exit time. We employ the convergence control method together with the dynamic programming algorithm to derive analytical expressions for the optimal portfolio policy and the mean-variance efficient frontier under certain conditions. We illustrate these results by an numerical example.
基金Work partially supported by a DGES Grant BSA2001-0803-C02-02
文摘Given a compact symmetric space, M, we obtain the mean exit time function from a principal orbit, for a Brownian particle starting and moving in a generalized ball whose boundary is the principal orbit. We also obtain the mean exit time flmction of a tube of radius r around special totally geodesic submanifolds P of M. Finally we give a comparison result for the mean exit time function of tubes around submanifolds in Riemannian manifolds, using these totally geodesic submanifolds in compact symmetric spaces as a model.
基金Supported partly by Grand-in-Aid for Scientific Research (C)
文摘We obtain upper and lower bounds of the exit times from balls of a jump-type symmetric Markov process. The proofs are delivered separately. The upper bounds are obtained by using the Levy system corresponding to the process, while the precise expression of the （L^2-）generator of the Dirichlet form associated with the process is used to obtain the lower bounds.
基金Supported by National Natural Science Foundation of China(Grant Nos.11001070,11101113)Zhejiang Provincial Natural Science Foundation(Grant No.R6090034)
文摘Let {Xn} be a Markov chain with transition probability pij =： aj-（i-1）＋,i,j ≥ 0, where aj=0 providedj 〈 0, a0 〉 0, a0＋a1〈 1 and ∑∞n=0 an= 1. Let μ∑∞n=1nan. It is known that {Xn} is positive recurrent when μ 〈 1; is null recurrent when μ= 1; and is transient when μ 〉 1. In this paper, the integrability of the first returning time and the last exit time are discussed. Keywords Geom/G/1 queuing model, first returning time, last exit time, Markov chain
文摘0 .Introduction The mathematical eqnivalenoe of Brownian切otion and olaosioal poten七ialtheory has great imPulsed the study of Potentials of Markov Prooesse
基金supported by Shanghai Municipal Government and Nokia
文摘Space time trellis coding （STTC） techniques have been proposed to achieve both diversity and coding gains in multiple input multiple output （MIMO） fading channels. But with more transmit antennas STTCs suffer from the design dificulty and complexity increasing. This paper proposes a scheme, named parallel concatenated space time trellis codes （PC-STTC）, to achieve the tradeoff between the performances and complexity of STTCs for a large number of transmit antennas. Simulation results and complexity comparison are provided to demonstrate the performance and superiority of the proposed scheme over conventional schemes in fast fading channels in low signal-to-noise ratio （SNR） regions. And an EXIT （extrinsic information transform） chart is given to analyze the iterative convergence of the proposed scheme. It shows that PC-STTC has better iterative convergence in low SNR regions.
文摘The motion of a lazy Pearson walker is studied with different probability (p) of jump in two and three dimensions. The probability of exit ( ) from a zone of radius is studied as a function of with different values of jump probability p. The exit probability is found to scale as , which is obtained by method of data collapse. The first passage time ( ) i.e., the time required for first exit from a zone is studied. The probability distribution of first passage time was studied for different values of jump probability (p). The probability distribution of first passage time was found to scale as . Where, F and G are two scaling functions and a, b, g and d are some exponents. In both the dimensions, it is found that, , , and .
基金Supported by NNSF of China (10001020 and 10471003), Foundation for Authors Awarded Excellent Ph.D.Dissertation
文摘Suppose X is a super-α-stable process in R^d, （0 〈 α〈 2）, whose branching rate function is dr, and branching mechanism is of the form ψ（z） = z^1＋β （0 〈0 〈β ≤1）. Let Xγ and Yγ denote the exit measure and the total weighted occupation time measure of X in a bounded smooth domain D, respectively. The absolute continuities of Xγ and Yγ are discussed.
文摘In this paper, we consider the two-sided first exit problem for jump diffusion processes having jumps with rational Laplace transforms. We investigate the probabilistic property of conditional memorylessness, and drive the joint distribution of the first exit time from an interval and the overshoot over the boundary at the exit time.
文摘Residence time in a flow measurement of radioactivity is the time spent by a pre-determined quantity of radioactive sample in the flow cell. In a recent report of the measurement of indoor radon by passive diffusion in an open volume (i.e. no flow cell or control volume), the concept of residence time was generalized to apply to measurement conditions with random, rather than directed, flow. The generalization, leading to a quantity Δtr, involved use of a) a phenomenological alpha-particle range function to calculate the effective detection volume, and b) a phenomenological description of diffusion by Fick’s law to determine the effective flow velocity. This paper examines the residence time in passive diffusion from the micro-statistical perspective of single-particle continuous Brownian motion. The statistical quantity “mean residence time” Tr is derived from the Green’s function for unbiased single-particle diffusion and is shown to be consistent with Δtr. The finite statistical lifetime of the randomly moving radioactive atom plays an essential part. For stable particles, Tr is of infinite duration, whereas for an unstable particle (such as 222Rn), with diffusivity D and decay rate λ, Tr is approximately the effective size of the detection region divided by the characteristic diffusion velocity . Comparison of the mean residence time with the time of first passage (or exit time) in the theory of stochastic processes shows the conditions under which the two measures of time are equivalent and helps elucidate the connection between the phenomenological and statistical descriptions of radon diffusion.
