Lévy Backward SDE Filter for Jump Diffusion Processes and Its Applications in Material Sciences

Authors

  • Feng Bao Department of Mathematics, Florida State University, Tallahassee, Florida, 32306, USA
  • Richard Archibald Computer Science and Mathematics Division, Oak Ridge, Tennessee, 37831, USA
  • Peter Maksymovych Center for Nanophase Material Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37831, USA

DOI:

https://doi.org/10.4208/cicp.OA-2018-0238

Keywords:

Nonlinear filtering problem, backward SDEs, jump diffusion processes, material sciences.

Abstract

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.

Published

2019-12-07

Issue

Section

Articles