LARGE DEVIATION PRINCIPLES FOR FIRST-ORDER SCALAR CONSERVATION LAWS WITH STOCHASTIC FORCING

• 成果类型: Article
• 署名作者: Dong, Zhao; Wu, Jiang-Lun; Zhang, Rangrang; Zhang, Tusheng
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Swansea University; Beijing Institute of Technology; University of Manchester
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1503
• 发表日期: 2020
• 页码: 324-367
• 关键词: equations

摘要

In this paper, we established the Freidlin-Wentzell-type large deviation principles for first-order scalar conservation laws perturbed by small multiplicative noise. Due to the lack of the viscous terms in the stochastic equations, the kinetic solution to the Cauchy problem for these first-order conservation laws is studied. Then, based on the well-posedness of the kinetic solutions, we show that the large deviations holds by utilising the weak convergence approach.