scholarly journals Analysis of a stochastic delay competition system driven by Lévy noise under regime switching

2017 ◽  
pp. 1-34
Author(s):  
Shiying Li ◽  
Shuwen Zhang
Keyword(s):  
Regime Switching ◽  
Lévy Noise ◽  
Stochastic Delay ◽  
Competition System ◽  
Levy Noise

Two impulsive stochastic delay single-species models incorporating Lévy noise

2018 ◽  
Vol 58 (1-2) ◽  
pp. 721-753 ◽  
Author(s):  
Huibin Lv ◽  
Zhijun Liu ◽  
Zuxiong Li ◽  
Lianwen Wang ◽  
Dashun Xu
Keyword(s):  
Single Species ◽  
Lévy Noise ◽  
Stochastic Delay ◽  
Levy Noise

Long-time behavior of Lévy-driven Ornstein–Uhlenbeck processes with regime switching

2020 ◽  
Vol 57 (1) ◽  
pp. 266-279
Author(s):  
Zhongwei Liao ◽  
Jinghai Shao
Keyword(s):  
Stationary Distribution ◽  
Regime Switching ◽  
Lévy Noise ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Lévy Measure ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Long Time ◽  
Levy Noise

AbstractWe investigate the long-time behavior of the Ornstein–Uhlenbeck process driven by Lévy noise with regime switching. We provide explicit criteria on the transience and recurrence of this process. Contrasted with the Ornstein–Uhlenbeck process driven simply by Brownian motion, whose stationary distribution must be light-tailed, both the jumps caused by the Lévy noise and the regime switching described by a Markov chain can derive the heavy-tailed property of the stationary distribution. The different role played by the Lévy measure and the regime-switching process is clearly characterized.

scholarly journals A stochastic delay Gilpin-Ayala competition system under regime switching

Filomat ◽  
2013 ◽  
Vol 27 (6) ◽  
pp. 955-964 ◽  
Author(s):  
Yiliang Liu ◽  
Qun Liu
Keyword(s):  
Regime Switching ◽  
Stochastic Delay ◽  
Competition System
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