南方科技大学知识苑(SUSTech KC): Backward doubly stochastic differential equations and SPDEs with quadratic growth

题名	Backward doubly stochastic differential equations and SPDEs with quadratic growth
作者	Hu，Ying 1; Wen，Jiaqiang2 ; Xiong，Jie2
通讯作者	Wen，Jiaqiang
发表日期	2024-09-01
DOI	10.1016/j.spa.2024.104405
发表期刊	Stochastic Processes and their Applications 影响因子和分区
ISSN	0304-4149
卷号	175
摘要	This paper shows the nonlinear stochastic Feynman–Kac formula holds under quadratic growth. For this, we initiate the study of backward doubly stochastic differential equations (BDSDEs, for short) with quadratic growth. The existence, uniqueness, and comparison theorem for one-dimensional BDSDEs are proved when the generator f(t,Y,Z) grows in Z quadratically and the terminal value is bounded, by introducing innovative approaches. Furthermore, in this framework, we utilize BDSDEs to provide a probabilistic representation of solutions to semilinear stochastic partial differential equations (SPDEs, for short) in Sobolev spaces, and use it to prove the existence and uniqueness of such SPDEs, thereby extending the nonlinear stochastic Feynman–Kac formula for linear growth introduced by Pardoux and Peng (1994).
关键词	Backward doubly stochastic differential equation Feynman–Kac formula Quadratic growth Sobolev solution Stochastic partial differential equation
相关链接	[Scopus记录]
收录类别	SCI ; EI
语种	英语
学校署名	通讯
EI入藏号	20242416258323
EI主题词	Nonlinear equations ; Partial differential equations ; Stochastic systems
EI分类号	Control Systems:731.1 ; Mathematics:921 ; Calculus:921.2 ; Systems Science:961
ESI学科分类	MATHEMATICS
Scopus记录号	2-s2.0-85195790255
来源库	Scopus
引用统计	被引频次[WOS]：1
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/778592
专题	理学院_数学系深圳国际数学中心（杰曼诺夫数学中心）（筹）
作者单位	1.University Rennes,CNRS,IRMAR - UMR 6625,Rennes,F-35000,France 2.Department of Mathematics and SUSTech International center for Mathematics,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China
通讯作者单位	数学系; 深圳国际数学中心（杰曼诺夫数学中心）（筹）
推荐引用方式 GB/T 7714	Hu，Ying,Wen，Jiaqiang,Xiong，Jie. Backward doubly stochastic differential equations and SPDEs with quadratic growth[J]. Stochastic Processes and their Applications,2024,175.
APA	Hu，Ying,Wen，Jiaqiang,&Xiong，Jie.(2024).Backward doubly stochastic differential equations and SPDEs with quadratic growth.Stochastic Processes and their Applications,175.
MLA	Hu，Ying,et al."Backward doubly stochastic differential equations and SPDEs with quadratic growth".Stochastic Processes and their Applications 175(2024).