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

Year:    2020

Author:    Feng Bao, Richard Archibald, Peter Maksymovych

Communications in Computational Physics, Vol. 27 (2020), Iss. 2 : pp. 589–618

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.

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

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

Communications in Computational Physics, Vol. 27 (2020), Iss. 2 : pp. 589–618

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    30

Keywords:    Nonlinear filtering problem backward SDEs jump diffusion processes material sciences.

Author Details

Feng Bao

Richard Archibald

Peter Maksymovych

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