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Asymptotics for stochastic reaction-diffusion equation driven by subordinate Brownian motions
Ran Wang1; Lihu Xu2,3
2018-10-06
Source PublicationStochastic processes and their applications
ISSN0304-4149
Volume128Issue:5Pages:1772-1796
Abstract

We study the ergodicity of stochastic reaction-diffusion equation driven by subordinate Brownian motions. 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 α-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.

KeywordStochastic Reaction-diffusion Equation Subordinate Brownian Motions Large Deviation Principle (Ldp) Occupation Measure
DOIhttps://doi.org/10.1016/j.spa.2017.08.010
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000430517900013
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
DEPARTMENT OF MATHEMATICS
Corresponding AuthorLihu Xu
Affiliation1.School of Mathematics and Statistics, Wuhan University, Wuhan, P.R. China
2.Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Macau
3.UM Zhuhai Research Institute, Zhuhai, China
Corresponding Author AffilicationFaculty of Science and Technology
Recommended Citation
GB/T 7714
Ran Wang,Lihu Xu. Asymptotics for stochastic reaction-diffusion equation driven by subordinate Brownian motions[J]. Stochastic processes and their applications,2018,128(5):1772-1796.
APA Ran Wang,&Lihu Xu.(2018).Asymptotics for stochastic reaction-diffusion equation driven by subordinate Brownian motions.Stochastic processes and their applications,128(5),1772-1796.
MLA Ran Wang,et al."Asymptotics for stochastic reaction-diffusion equation driven by subordinate Brownian motions".Stochastic processes and their applications 128.5(2018):1772-1796.
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