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Stochastic heat equation with Ornstein–Uhlenbeck operator
Li,Xiang
2023-10-01
Source PublicationStatistics and Probability Letters
ABS Journal Level2
ISSN0167-7152
Volume201Pages:109887
Abstract

We study the stochastic partial differential equation [Formula presented]=Lu+uẆ in Skorohod sense, where L is the generator of a one-dimensional Ornstein–Uhlenbeck (OU) process X and Ẇ is a (1+1)-dimensional space–time white noise. We follow the method established in Hu and Nualart (2009) to prove a Feynman–Kac type representation of the moments of solution. Through this representation, we use the method established in Chen (2015) and a large deviation principle of OU process to obtain an intermittency result.

KeywordFeynman–kac Representations Intermittency Ornstein–uhlenbeck Operator Stochastic Partial Differential Equation
DOI10.1016/j.spl.2023.109887
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:001032998200001
Scopus ID2-s2.0-85163505485
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Citation statistics
Document TypeJournal article
CollectionFaculty of Science and Technology
AffiliationDepartment of Mathematics,Faculty of Science and Technology,University of Macau,China
First Author AffilicationFaculty of Science and Technology
Recommended Citation
GB/T 7714
Li,Xiang. Stochastic heat equation with Ornstein–Uhlenbeck operator[J]. Statistics and Probability Letters, 2023, 201, 109887.
APA Li,Xiang.(2023). Stochastic heat equation with Ornstein–Uhlenbeck operator. Statistics and Probability Letters, 201, 109887.
MLA Li,Xiang."Stochastic heat equation with Ornstein–Uhlenbeck operator".Statistics and Probability Letters 201(2023):109887.
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