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Dynamical Analysis of Nonautonomous Trophic Cascade Chemostat Model with Regime Switching and Nonlinear Perturbations in a Polluted Environment: 《Acta Mathematicae Applicatae Sinica》2023年第3期550-570,共21页Ya-jie LI Hao-kun QI Zheng-bo CHANG Xin-zhu MENG; the National Natural Science Foundation of China (No.12271308);the Research Fund for the Taishan Scholar Project of Shandong Province of China;Shandong Provincial Natural Science Foundation of China (ZR2019MA003)。; This paper investigates the stochastic dynamics of trophic cascade chemostat model perturbed by regime switching, Gaussian white noise and impulsive toxicant input. For the system with only white noise interference, s...; 关键词：stochastic trophic cascade chemostat model Markov chain extinction and stochastic permanence periodic solution ERGODICITY

Multiple Ergodicity For Reversible Markov Chains: 《Acta Mathematicae Applicatae Sinica》2018年第4期863-868,共6页Yuan LIU; Supported by the National Natural Science Foundation of China(No.11431014,no.11688101);AMSS research grant(No.Y129161ZZ1);Key Laboratory of Random Complex Structures and Data,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(No.2008DP173182); Inspired by the multiple recurrence and multiple ergodic theorems for measure preserving systems,we discuss an analogous question for measure preserving semigroups. In this note, we deal with the symmetric semigroups ...; 关键词：Multiple recurrence reversible Markov chain

Adjoining Batch Markov Arrival Processes of a Markov Chain被引量：1: 《Acta Mathematicae Applicatae Sinica》2018年第1期1-10,共10页Xiao-yun MO Xu-yan XIANG Xiang-qun YANG; Supported by the National Natural Science Foundation of China(No.11671132,11601147);Hunan Provincial Natural Science Foundation of China(No.16J3010);Philosophy and Social Science Foundation of Hunan Province(No.16YBA053);Key Scientific Research Project of Hunan Provincial Education Department(No.15A032); A batch Markov arrival process（BMAP） X^＊=（N, J） is a 2-dimensional Markov process with two components, one is the counting process N and the other one is the phase process J. It is proved that the phase process i...; 关键词：Markov chain batch Markov arrival process （BMAP） adjoining BMAP fixed constant batch independent identically distributed （i.i.d） random batch

A Numerical Approach to Optimal Dividend Policies with Capital Injections and Transaction Costs被引量：1: 《Acta Mathematicae Applicatae Sinica》2017年第1期221-238,共18页Zhuo JIN Hai-liang YANG G.YIN; supported in part by Early Career Research Grant and Faculty Research Grant by The University of Melbourne;supported in part by Research Grants Council of the Hong Kong Special Administrative Region(project No.HKU 17330816);Society of Actuaries’Centers of Actuarial Excellence Research Grant;supported in part by U.S.Army Research Office under grant W911NF-15-1-0218; This work focuses on numerical methods for finding optimal dividend payment and capital injection policies to maximize the present value of the difference between the cumulative dividend payment and the possible capit...; 关键词：CONTROL singular control dividend policy capital injection free boundary Markov chain approx-imation

A Markov Copula Model with Regime Switching and Its Application: 《Acta Mathematicae Applicatae Sinica》2016年第1期163-174,共12页Xue LIANG; Supported by Jiangsu Government Scholarship for Overseas Studies;the NNSF of China(Grant Nos.11401419,11301369,11371274);the CPSF(2014M561453);the NSF of Jiangsu Province(Grant Nos.BK20140279,BK20130260); Regime switching,which is described by a Markov chain,is introduced in a Markov copula model.We prove that the marginals（X,H^i）,i = 1,2,3 of the Markov copula model（X,H） are still Markov processes and have marting...; 关键词：Markov copula model regime switching Markov chain credit default swap bilateral counterparty risk

Generalization Bounds of ERM Algorithm with Markov Chain Samples: 《Acta Mathematicae Applicatae Sinica》2014年第1期223-238,共16页Bin ZOU Zong-ben XU Jie XU; Supported by National 973 project(No.2013CB329404);Key Project of NSF of China(No.11131006);National Natural Science Foundation of China(No.61075054,61370000); One of the main goals of machine learning is to study the generalization performance of learning algorithms. The previous main results describing the generalization ability of learning algorithms are usually based on ...; 关键词：generalization bounds ERM algorithm relative uniform convergence uniformly ergodic Markovchain learning theory

A Single-server Discrete-time Retrial G-queue with Server Breakdowns and Repairs被引量：1: 《Acta Mathematicae Applicatae Sinica》2009年第4期675-684,共10页Jin-ting Wang Peng Zhang; Supported by the National Natural Science Foundation of China(No.10871020); This paper concerns a discrete-time Geo/Geo/1 retrial queue with both positive and negative customers where the server is subject to breakdowns and repairs due to negative arrivals. The arrival of a negative customer ...; 关键词：Discrete-time retrial queue G-queue Markov chain unreliable server

Asymptotic Expansions of Backward Equations for Two-time-scale Markov Chains in Continuous Time: 《Acta Mathematicae Applicatae Sinica》2009年第3期457-476,共20页Dung Tien Nguyen; supported in part by the National Science Foundation under DMS-0603287;inpart by the National Security Agency under grant MSPF-068-029;in part by the National Natural ScienceFoundation of China(No.70871055);supported in part by Wayne State University under Graduate ResearchAssistantship; This work develops asymptotic expansions for solutions of systems of backward equations of time- inhomogeneous Maxkov chains in continuous time. Owing to the rapid progress in technology and the increasing complexity ...; 关键词：Markov chain backward equation two-time scale asymptotic expansion

A Second-order Fluid Queue with Subordinator Input and Markov-modulated Linear Output: 《Acta Mathematicae Applicatae Sinica》2009年第2期345-352,共8页Jin-zhi Li; Supported by the National Natural Science Foundation of China(No.10726063); We consider an infinite capacity second-order fluid queue with subordinator input and Markovmodulated linear release rate. The fluid queue level is described by a generalized Langevin stochastic differential equation ...; 关键词：Second-order fluid queue SUBORDINATOR Markov chain linear release rate

Asymptotic Properties of Parabolic Systems for Null-Recurrent Switching Diffusions被引量：1: 《Acta Mathematicae Applicatae Sinica》2007年第2期177-194,共18页R.Z.Khasminskii; the National Science Foundation under DMS-0603287;the National Security Agency,MSPF-068-029; the National Natural Science Foundation of China under No.60574069; This work is concerned with the asymptotic behavior of systems of parabolic equations arising from null-recurrent switching diffusions, which are diffusion processes modulated by continuous-time Markov chains. A suffi...; 关键词：Parabolic system switching diffusion null recurrence Markov chain

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