Large deviations principle for stationary solutions of stochastic differential equations with multiplicative noise

Large deviations principle for stationary solutions of stochastic differential equations with multiplicative noise

We study the large deviations principle (LDP) for stationary solutions of a class of stochastic differential equations (SDE) in infinite time intervals by the weak convergence approach, and then establish the LDP for the invariant measures of the SDE by the contraction principle. We further point ou...

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Veröffentlicht in:arXiv.org 2022-06
Hauptverfasser: Gao, Peipei, Liu, Yong, Sun, Yue, Zheng, Zuohuan
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Deviation
Differential equations
Invariants
Mathematical analysis
Principles
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description We study the large deviations principle (LDP) for stationary solutions of a class of stochastic differential equations (SDE) in infinite time intervals by the weak convergence approach, and then establish the LDP for the invariant measures of the SDE by the contraction principle. We further point out the equivalence of the rate function of the LDP for invariant measures induced by the LDP for stationary solutions and the rate function defined by quasi-potential. This fact gives another view of the quasi-potential introduced by Freidlin and Wentzell.
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Invariants
Mathematical analysis
Principles
title Large deviations principle for stationary solutions of stochastic differential equations with multiplicative noise
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