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

Qi Zhang () and Huaizhong Zhao ()
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Qi Zhang: Fudan University
Huaizhong Zhao: Loughborough University

Journal of Theoretical Probability, 2012, vol. 25, issue 2, 396-423

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

Keywords: PDEs with polynomial growth coefficients; Generalized Feynman–Kac formula; Probabilistic representation of weak solutions; Backward stochastic differential equations; Weak convergence; Compact embedding; 60H10; 60H30; 35K55 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10959-011-0350-y

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