Probabilistic representation of weak solutions of partial differential equations with polynomial growth coefficients

Zhang, Qi; Zhao, Huaizhong

Abstract

In this paper we develop a new weak convergence and compact embedding method to study the existence and uniqueness of the L2p
ρ (Rd ;R1)×L2ρ(Rd ;Rd ) valued solution of backward stochastic differential equations with p-growth coefficients.
Then we establish the probabilistic representation of the weak solution of PDEs with p-growth coefficients via corresponding BSDEs.

Citation

Zhang, Q., & Zhao, H. (2012). Probabilistic representation of weak solutions of partial differential equations with polynomial growth coefficients. Journal of Theoretical Probability, 25, 396–423. https://doi.org/10.1007/s10959-011-0350-y

• Journal Article Type: Article
• Online Publication Date: Mar 17, 2011
• Publication Date: 2012-06
• Deposit Date: Oct 6, 2021
• Journal: Journal of Theoretical Probability
• Print ISSN: 0894-9840
• Electronic ISSN: 1572-9230
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 25
• Pages: 396–423
• DOI: https://doi.org/10.1007/s10959-011-0350-y
• Public URL: https://durham-repository.worktribe.com/output/1237214