%0 Journal Article
%A Bao, Feng
%A Cao, Yanzhao
%A Chi, Hongmei
%D 2019
%I Begell House
%K forward backward stochastic differential equation, jump diffusion processes, adjoint processes, Fokker-Planck equation
%N 2
%P 143-159
%R 10.1615/Int.J.UncertaintyQuantification.2019028300
%T ADJOINT FORWARD BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY JUMP DIFFUSION PROCESSES AND ITS APPLICATION TO NONLINEAR FILTERING PROBLEMS
%U http://dl.begellhouse.com/journals/52034eb04b657aea,3f762e845665d4bd,1df7b4ab3754a048.html
%V 9
%X Forward backward stochastic differential equations (FBSDEs) were first introduced as a probabilistic interpretation
for the Kolmogorov backward equation, and the solution of FBSDEs is equivalent to the solution of quasilinear partial
differential equations. In this work, we introduce the adjoint relation between a generalized FBSDE system driven
by jump diffusion processes and its time inverse adjoint FBSDE system under the probabilistic framework without
translating them into their corresponding PDEs. The "exact solution" of a nonlinear filtering problem is derived as an
application.
%8 2019-04-23