A stochastic representation for fully nonlinear PDEs and its application to homogenization

Journal of Mathematical Sciences

Ichihara, Naoyuki¹ 

关键词: Fully nonlinear parabolic equations;    Hamilton-Jacobi-Bellman equations;    backward stochastic differential equations;    nonlinear Feynman-Kac formula;    homogenization;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

Weestablishastochasticrepresentationformulaforsolutionstofullynonlinearsecond-orderpartialdifferentialequationsofparabolictype.Forthispurpose,weintroduceforward-backwardstochasticdifferentialequationswithrandomcoefficients.Wenextapplythemtohomogenizationoffullynonlinearparabolicequations.Asabyproduct,weobtainanestimateconcerningtheconvergencerateofsolutions.TheresultspartiallygeneralizehomogenizationofHamilton-Jacobi-BellmanequationsstudiedbyR.Buckdahnandtheauthor.

【 授权许可】

Unknown