MCRF
Semi-linear backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process
Shaokuan Chen Shanjian Tang
Mathematical Control & Related Fields 2015, 5(3): 401-434 doi: 10.3934/mcrf.2015.5.401
In this paper we investigate classical solution of a semi-linear system of backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process. By proving an Itô-Wentzell formula for jump diffusions as well as an abstract result of stochastic evolution equations, we obtain the stochastic integral partial differential equation for the inverse of the stochastic flow generated by a stochastic differential equation driven by a Brownian motion and a Poisson point process. By composing the random field generated by the solution of a backward stochastic differential equation with the inverse of the stochastic flow, we construct the classical solution of the system of backward stochastic integral partial differential equations. As a result, we establish a stochastic Feynman-Kac formula.
keywords: stochastic differential equation Poisson point process Backward stochastic integral partial differential equation backward stochastic differential equation stochastic flow Itô-Wentzell formula.

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