Irreducibility of Stochastic Complex Ginzburg-Landau Equations Driven by Pure Jump Noise and Its Applications

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-03-19 DOI:10.1007/s00245-024-10115-8

Hao Yang, Jian Wang, Jianliang Zhai

引用次数: 0

Abstract

Considering irreducibility is fundamental for studying the ergodicity of stochastic dynamical systems. In this paper, we establish the irreducibility of stochastic complex Ginzburg-Laudau equations driven by pure jump noise. Our results are dimension free and the conditions placed on the driving noises are very mild. A crucial role is played by criteria developed by the authors of this paper and T. Zhang for the irreducibility of stochastic equations driven by pure jump noise. As an application, we obtain the ergodicity of stochastic complex Ginzburg-Laudau equations. We remark that our ergodicity result covers the weakly dissipative case with pure jump degenerate noise.

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纯跳跃噪声驱动的随机复杂金兹堡-朗道方程的不可还原性及其应用

考虑不可还原性是研究随机动力系统遍历性的基础。在本文中，我们建立了由纯跳跃噪声驱动的随机复数金兹堡-劳道方程的不可还原性。我们的结果是无维度的，对驱动噪声的条件也非常温和。本文作者和 T. Zhang 针对纯跳跃噪声驱动的随机方程的不可还原性制定的标准发挥了至关重要的作用。作为应用，我们得到了随机复数金兹堡-劳道方程的遍历性。我们指出，我们的遍历性结果涵盖了纯跳跃退化噪声的弱耗散情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.