Non-autonomous stochastic lattice systems with Markovian switching

Li, Dingshi; Lin, Yusen; Pu, Zhe

doi:10.3934/dcds.2022181

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2024

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Cited by 3 publications

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“…This enables SLDEs to better reveal objective phenomena. For this reasing, SLDEs have attracted extensive attention; see [3,4,8,14,15,26].…”

Section: Introductionmentioning

confidence: 99%

Periodic solutions in distribution for stochastic lattice differential equations

Gao,

Yang

2024

ejde

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“…This enables SLDEs to better reveal objective phenomena. For this reasing, SLDEs have attracted extensive attention; see [3,4,8,14,15,26].…”

Section: Introductionmentioning

confidence: 99%

Periodic solutions in distribution for stochastic lattice differential equations

Gao,

Yang

2024

ejde

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show abstract

Invariant measures and large deviation principles for stochastic Schrödinger delay lattice systems

Chen,

Sun,

Wang

2024

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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This paper is concerned with stochastic Schrödinger delay lattice systems with both locally Lipschitz drift and diffusion terms. Based on the uniform estimates and the equicontinuity of the segment of the solution in probability, we show the tightness of a family of probability distributions of the solution and its segment process, and hence the existence of invariant measures on $l^2\times L^2((-\rho,\,0);l^2)$ with $\rho >0$ . We also establish a large deviation principle for the solutions with small noise by the weak convergence method.

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Dynamical behaviors of an impulsive stochastic neural field lattice model

Zeng,

Mi,

2024

Stoch. Dyn.

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This paper is concerned with the asymptotic behaviors of the solutions of an impulsive stochastic neural field lattice model driven by nonlinear noise. We first show the existence and uniqueness of weak pullback mean random attractors for the impulsive stochastic systems. Then by the properties of Markov processes, the existence of evolution system of measures for the impulsive stochastic systems is established. To this end, we employ the idea of uniform estimates on the tails of the solutions to show the tightness of a family of distributions of the solutions of the lattice systems.

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Non-autonomous stochastic lattice systems with Markovian switching

Cited by 3 publications

References 20 publications

Periodic solutions in distribution for stochastic lattice differential equations

Periodic solutions in distribution for stochastic lattice differential equations

Invariant measures and large deviation principles for stochastic Schrödinger delay lattice systems

Dynamical behaviors of an impulsive stochastic neural field lattice model

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