Backward SDE Filter for Jump Diffusion Processes and Its Applications in Material Sciences
This work offers a novel theoretical framework for optimal filtering in jump diffusion processes, relevant to material sciences and stochastic systems.
The paper establishes a connection between forward backward doubly stochastic differential equations and optimal filtering for jump diffusion processes, providing a new representation of the unnormalized filtering density without relying on Zakai's equation.
The connection between forward backward doubly stochastic differential equations and the optimal filtering problem is established without using the Zakai's equation. The solutions of forward backward doubly stochastic differential equations are expressed in terms of conditional law of a partially observed Markov diffusion process. It then follows that the adjoint time-inverse forward backward doubly stochastic differential equations governs the evolution of the unnormalized filtering density in the optimal filtering problem.