On limiting behavior of stationary measures for stochastic evolution systems with small noise intensity

By Lifeng Chen, Zhao Dong, Jifa Jiang, Jianliang Zhai. Science China Mathematics, 2016

55 citations recorded by the source corpus.

The limiting behavior of stochastic evolution processes with small noise intensity ϵ is investigated in distribution-based approaches. Let μϵ be a stationary measure for stochastic process Xϵ with small ϵ and X0 be a semiflow on a Polish space. Assume that {μϵ: 0 < ϵ ⩽ ϵ0} is tight. Then all their limits in the weak sense are X0-invariant and their supports are contained in the Birkhoff center of X0. Applications are made to various stochastic evolution systems, including stochastic ordinary differential equations, stochastic partial differential equations, and stochastic functional differential equations driven by Brownian motion or Lévy processes.

Subfields: Computational Theory and Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/be6871c935e09a8705617080fe96656d48e2b920

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In Computational Theory and Mathematics

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In Finance

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Citations in the corpus

• Limiting Behavior of Invariant Measures of Stochastic Delay Lattice Systems (2021, background): “As in [13], we assume that for every compact set K ⊆ Z , t ≥ 0, ε0 ∈ [0, 1] and η > 0, lim ε→ε0 sup x∈K P ( d ( X (t, 0, x) , X0 (t, 0, x) ) ≥ η = 0.”