Stationary distribution and ergodicity of a stochastic hybrid competition model with Lévy jumps

2018 ◽  
Vol 30 ◽  
pp. 225-239 ◽  
Author(s):  
Meng Liu ◽  
Yu Zhu
Keyword(s):  
Stationary Distribution ◽  
Competition Model ◽  
Stationary Distribution And Ergodicity ◽  
Lévy Jumps

The stationary distribution and ergodicity of a stochastic mutualism model

2018 ◽  
Vol 68 (3) ◽  
pp. 685-690 ◽  
Author(s):  
Jingliang Lv ◽  
Sirun Liu ◽  
Heng Liu
Keyword(s):  
Stochastic Model ◽  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Ergodic Property ◽  
Model Simulations ◽  
Analytical Results ◽  
Stationary Distribution And Ergodicity ◽  
Mutualism Model ◽  
Mutualism System

Abstract This paper is concerned with a stochastic mutualism system with toxicant substances and saturation terms. We obtain the sufficient conditions for the existence of a unique stationary distribution to the equation and it has an ergodic property. It is interesting and surprising that toxicant substances have no effect on the stationary distribution of the stochastic model. Simulations are also carried out to confirm our analytical results.

scholarly journals Stationarity and Ergodicity for an Affine Two-Factor Model

2014 ◽  
Vol 46 (03) ◽  
pp. 878-898 ◽  
Author(s):  
Mátyás Barczy ◽  
Leif Döring ◽  
Zenghu Li ◽  
Gyula Pap
Keyword(s):  
Stationary Distribution ◽  
Factor Model ◽  
Two Dimensional ◽  
Affine Process ◽  
Stationary Distribution And Ergodicity ◽  
Coordinate Process

We study the existence of a unique stationary distribution and ergodicity for a two-dimensional affine process. Its first coordinate process is supposed to be a so-called α-root process with α ∈ (1, 2]. We prove the existence of a unique stationary distribution for the affine process in the α ∈ (1, 2] case; furthermore, we show ergodicity in the α = 2 case.

scholarly journals Permanence of a stochastic delay competition model with Levy jumps

2017 ◽  
Vol 10 (06) ◽  
pp. 3245-3260
Author(s):  
Meng Liu ◽  
Meiling Deng ◽  
Zhaojuan Wang
Keyword(s):  
Competition Model ◽  
Stochastic Delay ◽  
Lévy Jumps
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