华东师范大学学报（自然科学版） >

2025 , Vol. 2025 >Issue 1: 1 - 12

DOI: https://doi.org/10.3969/j.issn.1000-5641.2025.01.001

数学

一类具有负跳的α-稳定过程驱动的种群模型的遍历性

  • 童金英 ,
  • 梁子翼 ,
  • 陈文泽 ,
  • 张振中 ,
  • 赵馨
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  • 1. 东华大学 数学与统计学院, 上海　201620
    2. 上海人工智能网络系统工程技术研究中心, 上海　201203
童金英, 女, 副教授, 研究方向为马尔可夫过程的遍历性. E-mail: jytong@dhu.edu.cn

收稿日期: 2024-01-07

  网络出版日期: 2025-01-20

基金资助

国家自然科学基金 (12171081); 上海市自然科学基金(23ZR1402600); 上海市启明星计划扬帆专项 (22YF1400900); 东华大学虚拟仿真实验教学项目

版权

华东师范大学学报期刊社, 2025, 版权所有，未经授权，不得转载、摘编本刊文章，不得使用本刊的版式设计。
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Ergodicity for population dynamics driven by a class of $\alpha $ -stable process with negative jumps

  • Jinying TONG ,
  • Ziyi LIANG ,
  • Wenze CHEN ,
  • Zhenzhong ZHANG ,
  • Xin ZHAO
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  • 1. School of Mathematics and Statistics, Donghua University, Shanghai　201620, China
    2. Shanghai Engineering Research Center of Artificial Intelligence Network, Shanghai　201203, China

Received date: 2024-01-07

  Online published: 2025-01-20

Copyright

, 2025, Copyright reserved © 2025.
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摘要

为拟合随机环境与重大因素的影响, 基于马氏链与带负跳$\alpha$ - 稳定过程, 建立了一类种群互惠模型. 首先, 证明了该种群模型具有全局正解性; 其次, 给出了该模型的遍历性的充分条件.

关键词： $\alpha $ -稳定过程; 马氏链; 遍历性; 负跳

本文引用格式

童金英 , 梁子翼 , 陈文泽 , 张振中 , 赵馨 . 一类具有负跳的α-稳定过程驱动的种群模型的遍历性[J]. 华东师范大学学报（自然科学版）, 2025 , 2025(1) : 1 -12 . DOI: 10.3969/j.issn.1000-5641.2025.01.001

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

参考文献

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