J* E* C* N* U* N* S* ›› 2025, Vol. 2025 ›› Issue (1): 1-12.doi: 10.3969/j.issn.1000-5641.2025.01.001

• Mathematics •    

Ergodicity for population dynamics driven by a class of $\alpha $ -stable process with negative jumps

Jinying TONG1(), Ziyi LIANG1, Wenze CHEN1, Zhenzhong ZHANG1, Xin ZHAO1,2   

  1. 1. School of Mathematics and Statistics, Donghua University, Shanghai 201620, China
    2. Shanghai Engineering Research Center of Artificial Intelligence Network, Shanghai 201203, China
  • Received:2024-01-07 Online:2025-01-25 Published:2025-01-20

Abstract:

In order to characterize that stochastic environment, we consider a class facultative population systems driven by Markov chains and pure-jump stable processes with negative jumps. To begin with, the existence and uniqueness for global positive solution is proved for our model. Then, some sufficient conditions for stationary distribution are provided.

Key words: $\alpha $ -stable processes, Markov chains, ergodicity, negative jumps

CLC Number: