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ergodicity of a Class of Nonlinear Time Series Models in Random Environment Domain

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Acta Mathematicae Applicatae Sinica 2010年第1期26卷 159-168页

作者： En-wen Zhu Han-jun Zhang Gang Yang Zai-ming Liu Jie-zhong Zou Shao-shun Long School of Mathematics and Computational Science Xiangtan University Hunan 411105 China School of Mathematics and Computing Sciences Changsha University of Science and Technology Hunan410076 China School of Information Hunan University of Commerce Hunan 410205 China School of Mathematics Central South University Hunan 410075 China

In this paper, we study the problem of a variety of p, onlinear time series model Xn＋ 1= TZn＋1（X（n）, … ,X（n - Zn＋l）, en＋1（Zn＋1）） in which {Zn} is a Markov chain with finite state space, and for every state i of the Markov chain, {en（i）} is a sequence of independent and identically distributed random variables. Also, the limit behavior of the sequence {Xn} defined by the above model is investigated. Some new novel results on the underlying models are presented.

关键词： ergodicity Random environment Nonlinear time series

ergodicity of the 2D Navier-Stokes Equations with Degenerate Multiplicative Noise

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Acta Mathematicae Applicatae Sinica 2018年第1期34卷 97-118页

作者： Zhao DONG Xu-hui PENG RCSDS Academy of Mathematics and Systems Science Chinese Academy of Sciences China Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China) College of Mathematics and Computer Science Hunan Normal University Changsha 410081. China School of Mathematics Sciences University of Chinese Academy of Sciences Beijing 100190 China

Consider the two-dimensional, incompressible Navier-Stokes equations on torus T^2= [-π, π]^2 driven by a degenerate multiplicative noise in the vorticity formulation（abbreviated as SNS）： dwt = ν？w_tdt ＋B（Kw_t, w_t）dt ＋ Q（w_t）dW t. We prove that the solution to SNS is continuous differentiable in initial value. We use the Malliavin calculus to prove that the semigroup{P_t}_t≥0 generated by the SNS is asymptotically strong Feller. Moreover, we use the coupling method to prove that the solution to SNS has a weak form of *** almost the same Hypotheses as that given by Odasso, Prob. Theory Related Fields, 140： 41–82（2005）with a different method, we get an exponential ergodicity under a stronger norm.

关键词： tochastic Navier-Stokes equation asymptotically strong Feller property ergodicity

ergodicity of Quasi-birth and Death Processes(Ⅰ)

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Acta Mathematica Sinica,English Series 2007年第2期23卷 201-208页

作者： Zhen Ting HOU Xiao Hua LI School of Mathematics Central South University School of science Beijing University of Posts and Telecommunications

Quasi-birth and death processes with block tridiagonal matrices find many applications in various areas. Neuts gave the necessary and sufficient conditions for the ordinary ergodicity and found an expression of the stationary distribution for a class of quasi-birth and death processes. In this paper we obtain the explicit necessary and sufficient conditions for/-ergodicity and geometric ergodicity for the class of quasi-birth and death processes, and prove that they are not strongly ergodic. Keywords ergodicity, quasi-birth and death process.

关键词： ergodicity quasi-birth and death process Markov chain matrix geometric solutions

ergodicity for Infinite-dimensional Diffusion Processes on Manifolds

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Science China Mathematics 1994年第2期37卷 137-146页

作者：王风雨 Department of Mathematics.Beijing Normal University Beijing 100875PRC

In this paper,the coupling method is used to study the ergodicity for infinite dimensional diffusion processes on manifolos The result presented here improves,in some interesting cases,the results obtained by Deuschel... 详细信息

关键词： ergodicity diffusion process coupling Gibbs state

A one-time one-key encryption algorithm based on the ergodicity of chaos

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Chinese Physics B 2012年第2期21卷 148-152页

作者：王兴元腾琳 Faculty of Electronic Information and Electrical Engineering Dalian University of TechnologyDalian 116024China

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.

关键词： chaos encryption ergodicity

The ergodicity of a Class of Almost Anosov Systems

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Acta Mathematica Sinica,English Series 2013年第1期29卷 193-198页

作者： Yun Hua ZHOU College of Mathematics and Statistics Chongqing University

In this paper, we prove that some volume-preserving almost Anosov systems are ergodic if they are essentially accessible. The key idea is that there are stable and unstable manifolds with uniform size on the orbits Of... 详细信息

关键词： ergodicity almost Anosov essential accessibility

V-uniform ergodicity for fluid queues

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Applied Mathematics(A Journal of Chinese Universities) 2019年第1期34卷 82-91页

作者： LIU Yuan-yuan LI Yang School of Mathematics and Statistics New Campus Central South University

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.

关键词： uid queues QBD processes ergodicity the extended generator

UNIQUENESS, ergodicity AND UNIDIMENSIONALITY OF INVARIANT MEASURES UNDER A MARKOV OPERATOR

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Acta Mathematica Scientia 2009年第5期29卷 1309-1322页

作者：唐军民张继宏章雄鹰 School of Mathematics and Statistics Wuhan University Institute of Mathematics Hangzhou Dianzi University Department of Mathematics South China University of Technology

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.

关键词： Markov operator invariant measure ergodicity unidimensionality

THE ergodicity OF STOCHASTIC GENERALIZED POROUS MEDIA EQUATIONS WITH LVY JUMP

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Acta Mathematica Scientia 2011年第3期31卷 925-933页

作者：周国立侯振挺 School of Mathematics Central South University College of Mathematics and Statistis Changqing University

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 equ... 详细信息

关键词： stochastic porous medium equation Lévy processes ergodicity