Ergodicity of one-dimensional regime-switching diffusion processes

2014 ◽  
Vol 57 (11) ◽  
pp. 2407-2414 ◽  
Author(s):  
JingHai Shao
Keyword(s):  
Regime Switching ◽  
Diffusion Processes ◽  
One Dimensional ◽  
Switching Diffusion

Permanence and extinction of stochastic regime-switching mutualism model

2020 ◽  
Vol 13 (04) ◽  
pp. 2050028
Author(s):  
Guangying Lv ◽  
Beibei Zhang
Keyword(s):  
Regime Switching ◽  
Diffusion Processes ◽  
Sufficient Conditions ◽  
Switching Diffusion ◽  
Random Switching ◽  
The Difference ◽  
Mutualism Model

This paper is concerned with the permanence and extinction of a stochastic regime-switching mutualism model. We aim to find the difference between the stochastic mutualism model with regime-switching and without regime-switching. By studying ergodicity of regime-switching diffusion processes, we establish the sufficient conditions to estimate the permanence and extinction of a species in a random switching environment. Moreover, compared with the system without switching, the advantages of the stochastic regime-switching mutualism model are given.

scholarly journals Exponential ergodicity for regime-switching diffusion processes in total variation norm

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jun Li ◽  
Fubao Xi
Keyword(s):  
Probability Measure ◽  
Total Variation ◽  
Regime Switching ◽  
Diffusion Processes ◽  
Invariant Probability Measure ◽  
Stability And Convergence ◽  
Time Behavior ◽  
Total Variation Norm ◽  
Switching Diffusion ◽  
Variation Norm

<p style='text-indent:20px;'>We investigate the long time behavior for a class of regime-switching diffusion processes. Based on direct evaluation of moments and exponential functionals of hitting time of the underlying process, we adopt coupling method to obtain existence and uniqueness of the invariant probability measure and establish explicit exponential bounds for the rate of convergence to the invariant probability measure in total variation norm. In addition, we provide some concrete examples to illustrate our main results which reveal impact of random switching on stochastic stability and convergence rate of the system.</p>

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