TY - JOUR
T1 - Lévy Backward SDE Filter for Jump Diffusion Processes and Its Applications in Material Sciences
AU - Bao , Feng
AU - Archibald , Richard
AU - Maksymovych , Peter
JO - Communications in Computational Physics
VL - 2
SP - 589
EP - 618
PY - 2019
DA - 2019/12
SN - 27
DO - http://doi.org/10.4208/cicp.OA-2018-0238
UR - https://global-sci.org/intro/article_detail/cicp/13460.html
KW - Nonlinear filtering problem, backward SDEs, jump diffusion processes, material sciences.
AB - <p style="text-align: justify;">We develop a novel numerical method for solving the nonlinear filtering
problem of jump diffusion processes. The methodology is based on numerical approximation of backward stochastic differential equation systems driven by jump diffusion
processes and we apply adaptive meshfree approximation to improve the efficiency of
numerical algorithms. We then use the developed method to solve atom tracking problems in material science applications. Numerical experiments are carried out for both
classic nonlinear filtering of jump diffusion processes and the application of nonlinear
filtering problems in tracking atoms in material science problems.</p>