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

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 noi...

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Bibliographic Details
Published in:Applied mathematics & optimization 2024-04, Vol.89 (2), p.47, Article 47
Main Authors: Yang, Hao, Wang, Jian, Zhai, Jianliang
Format: Article
Language:English
Subjects:
Applied mathematics
Calculus of Variations and Optimal Control
Optimization
Control
Ergodic processes
Landau-Ginzburg equations
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Noise
Numerical and Computational Physics
Optimization
Phase transitions
Simulation
Stochastic systems
Systems Theory
Theoretical
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Summary: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.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-024-10115-8