Large Deviation Principle for McKean-Vlasov Quasilinear Stochastic Evolution Equations
Large Deviation Principle for McKean-Vlasov Quasilinear Stochastic Evolution Equations
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DOI：
10.1007/s00245-021-09796-2
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发表时间：
2021-07-02
影响因子：
1.8
通讯作者：
Liu, Wei
中科院分区：
文献类型：
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作者：
Hong, Wei;Li, Shihu;Liu, Wei
研究了一类受乘性噪声扰动的McKean-Vlasov拟线性随机偏微分方程的Freidlin-Wentzell大偏差原理。采用变分框架和修正的弱收敛准则证明了McKean-Vlasov型随机偏微分方程的拉普拉斯原理，该原理等价于大偏差原理.此外，我们没有假设任何紧性条件的嵌入在Gelfand三元组处理的情况下，有界和无界域的应用。主要结果可应用于各种McKean-Vlasov型随机偏微分方程，如分布相关的随机多孔介质型方程和随机p-Laplace型方程。
This paper is devoted to investigating the Freidlin-Wentzell's large deviation principle for a class of McKean-Vlasov quasilinear SPDEs perturbed by small multiplicative noise. We adopt the variational framework and the modified weak convergence criteria to prove the Laplace principle for McKean-Vlasov type SPDEs, which is equivalent to the large deviation principle. Moreover, we do not assume any compactness condition of embedding in the Gelfand triple to handle both the cases of bounded and unbounded domains in applications. The main results can be applied to various McKean-Vlasov type SPDEs such as distribution dependent stochastic porous media type equations and stochastic p-Laplace type equations.