Asymptotics for stochastic reaction-diffusion equation driven by subordinate Brownian motion

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Wang, Ran¹  Xu, Lihu^2,3 

[1] Wuhan Univ, Sch Math & Stat, Wuhan, Hubei, Peoples R China

[2] Univ Macau, Fac Sci & Technol, Dept Math, Taipa, Macao, Peoples R China

[3] UM Zhuhai Res Inst, Zhuhai, Peoples R China

关键词: Stochastic reaction-diffusion equation;    Subordinate Brownian motions;    Large deviation principle;    Occupation measure;   

DOI  :  10.1016/j.spa.2017.08.010

来源: Elsevier

【 摘 要 】

We study the ergodicity of stochastic reaction-diffusion equation driven by subordinate Brownian motion. After establishing the strong Feller property and irreducibility of the system, we prove the tightness of the solution's law. These properties imply that this stochastic system admits a unique invariant measure according to Doob's and Krylov-Bogolyubov's theories. Furthermore, we establish a large deviation principle for the occupation measure of this system by a hyper-exponential recurrence criterion. It is well known that S(P)DEs driven by alpha-stable type noises do not satisfy Freidlin-Wentzell type large deviation, our result gives an example that strong dissipation overcomes heavy tailed noises to produce a Donsker- Varadhan type large deviation as time tends to infinity. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

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