ADJOINT FORWARD BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY JUMP DIFFUSION PROCESSES AND ITS APPLICATION TO NONLINEAR FILTERING PROBLEMS

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...