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

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

2009-02-06

arxiv.org/abs/0902.1148v3

Mathematics

Probability

Scientific paper

10.1007/s10959-011-0350-y

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.

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