Probabilistic Representation of Weak Solutions of Partial Differential Equations with Polynomial Growth Coefficients

Abstract

In this paper we develop a new weak convergence and compact embedding method to study the existence and uniqueness of the $L_{\rho }^2({\mathbb{R}}^d;{\mathbb{R}}^1)\otimes L_{\rho }^2({\mathbb{R}}^d;{\mathbb{R}}^d)$ 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.

References in corpus (2)

• BSDE with quadratic growth and unbounded terminal value
• Stationary Solutions of SPDEs and Infinite Horizon BDSDEs

Cited by in corpus (3)

• Time discretization of FBSDE with polynomial growth drivers and reaction-diffusion PDEs
• A study of backward stochastic differential equation on a Riemannian manifold
• Stationary Stochastic Viscosity Solutions of SPDEs