The Stationary Distribution of Competitive Lotka-Volterra Population Systems with Jumps

Abstract and Applied Analysis ◽

10.1155/2014/820831 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7

Author(s):

Zhenzhong Zhang ◽

Jinying Tong ◽

Jianhai Bao

Keyword(s):

Stationary Distribution ◽

Asymptotic Properties ◽

Pathwise Estimation

Dynamics of Lotka-Volterra population with jumps (LVWJ) have recently been established (see Bao et al., 2011, and Bao and Yuan, 2012). They provided some useful criteria on the existence of stationary distribution and some asymptotic properties for LVWJ. However, the uniqueness of stationary distribution forn≥2and asymptotic pathwise estimationlimt→+∞⁡(1/t)∫0t‍|X(s)|pds (p>0)are still unknown for LVWJ. One of our aims in this paper is to show the uniqueness of stationary distribution and asymptotic pathwise estimation for LVWJ. Moreover, some characterizations for stationary distribution are provided.

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Quotients of Markov chains and asymptotic properties of the stationary distribution of the Markov chain associated to an evolutionary algorithm

Genetic Programming and Evolvable Machines ◽

10.1007/s10710-007-9038-6 ◽

2007 ◽

Vol 9 (2) ◽

pp. 109-123 ◽

Cited By ~ 6

Author(s):

Boris Mitavskiy ◽

Jonathan E. Rowe ◽

Alden Wright ◽

Lothar M. Schmitt

Keyword(s):

Markov Chain ◽

Markov Chains ◽

Evolutionary Algorithm ◽

Stationary Distribution ◽

Asymptotic Properties

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Stationary distribution and pathwise estimation of n-species mutualism system with stochastic perturbation

The Journal of Nonlinear Sciences and Applications ◽

10.22436/jnsa.009.04.47 ◽

2016 ◽

Vol 09 (04) ◽

pp. 1936-1943 ◽

Cited By ~ 1

Author(s):

Weiwei Fang ◽

Qixing Han ◽

Xiangdan Wen ◽

Qiuyue Li

Keyword(s):

Stationary Distribution ◽

Stochastic Perturbation ◽

Pathwise Estimation ◽

Mutualism System

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Asymptotic properties of the maximum-likelihood estimator for a class of birth-and-death processes admitting a unique stationary distribution

Canadian Journal of Statistics ◽

10.2307/3314977.n ◽

1983 ◽

Vol 11 (2) ◽

pp. 109-118

Author(s):

O. Brian Allen

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimator ◽

Stationary Distribution ◽

Asymptotic Properties ◽

Likelihood Estimator ◽

Birth And Death Processes

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Stability and ergodicity of a stochastic Gilpin–Ayala model under regime switching on patches

International Journal of Biomathematics ◽

10.1142/s1793524517500905 ◽

2017 ◽

Vol 10 (06) ◽

pp. 1750090 ◽

Cited By ~ 2

Author(s):

Adel Settati ◽

Aadil Lahrouz

Keyword(s):

Equilibrium State ◽

Global Stability ◽

Computer Simulations ◽

Stationary Distribution ◽

Regime Switching ◽

Asymptotic Properties ◽

System Model ◽

Population System ◽

Analytical Results ◽

Trivial Equilibrium

The purpose of this work is to investigate the asymptotic properties of a stochastic Gilpin–Ayala population system under regime switching on patches. We establish the global stability and the extinction of the trivial equilibrium state of the model. Furthermore, we show the existence of the stationary distribution for our system model. The analytical results are illustrated by computer simulations.

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Normal approximations to discrete unimodal distributions

Journal of Applied Probability ◽

10.1017/s0021900200115931 ◽

1986 ◽

Vol 23 (04) ◽

pp. 1013-1018

Author(s):

B. G. Quinn ◽

H. L. MacGillivray

Keyword(s):

Stationary Distribution ◽

Sufficient Conditions ◽

Random Variables ◽

Hypergeometric Distribution ◽

Death Process ◽

Normal Approximations ◽

Discrete Random Variables ◽

Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

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