BSDE's and viscosity solutions of semilinear pde's

Abstract

In this paper, we study the existence and uniqueness of solutions of systems of semilinear PDE's by a probabilistic method based upon the nonlinear Feynman-Kac formula, introduced by E. Pardoux and S. Peng in [13]. Our contribution to this topic is to weaken the Lipschitz assumption on the coefficients of the linear part of the operator, assuming nevertheless the existence of a Lyapunov function to ensure the non-explosion of the associated diffusion process. This extension was motivated by problems arising in stochastic dynamical systems theory

Keywords:

• Lyapunov functions
• nonexplosion of solutions of stochastic differential equations
• backward stochastic differential equations
• viscosity solutions of systems of nonlinear partial differential equations
• AMS Classification: 60H10, 60H30, 35K55, 93D30