This study investigates mean-square random invariant manifolds in stochastic differential equations, showing significant implications for random dynamical systems.
This paper aims to investigate the mean-square invariant manifolds for a class of stochastic differential equations with jumps. We first prove the existence of mean-square random invariant unstable manifolds for mean-square random dynamical systems, which involves the filtration generated by both a Brownian motion and a Poisson random measure. Then, we establish the existence of mean-square random stable invariant sets.
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Wu et al. (2025) studied this question.
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