Lévy Backward SDE Filter for Jump Diffusion Processes and Its Applications in Material Sciences (Communications in Computational Physics, 2019)
We develop a novel numerical method for solving the nonlinear filteringproblem of jump diffusion processes. The methodology is based on numerical approximation of backward stochastic differential equation systems driven by jump diffusionprocesses and we apply adaptive meshfree approximation to improve the efficiency ofnumerical algorithms. We then use the developed method to solve atom tracking problems in material science applications. Numerical experiments are carried out for bothclassic nonlinear filtering of jump diffusion processes and the application of nonlinearfiltering problems in tracking atoms in material science problems.
Keywords: Nonlinear filtering problem; backward SDEs; jump diffusion processes; material sciences.