Lévy backward SDE filter for jump diffusion processes and its applications in material sciences

Feng Bao; Richard Archibald; Peter Maksymovych

doi:10.4208/cicp.OA-2018-0238

Lévy backward SDE filter for jump diffusion processes and its applications in material sciences

Feng Bao, Richard Archibald, Peter Maksymovych

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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.

Original language	English
Pages (from-to)	589-618
Number of pages	30
Journal	Communications in Computational Physics
Volume	27
Issue number	2
DOIs	https://doi.org/10.4208/cicp.OA-2018-0238
State	Published - 2020

Funding

acknowledges support by the Center for Nanophase Materials Sciences, sponsored by the Division of User Facilities, Basic Energy Sciences, U.S. Department of Energy. This work was supported in part by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) program through the FASTMath Institute (under Lawrence Livermore National Laboratory Subcontract B626484). The first author acknowledges support by U.S. National Science Foundation under grant number DMS-1720222 and support by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, SciDAC program through the CompFUSE project. The third author also This work was supported in part by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) program through the FASTMath Institute (under Lawrence Livermore National Laboratory Subcontract B626484). The first author acknowledges support by U.S. National Science Foundation under grant number DMS-1720222 and support by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, SciDAC program through the CompFUSE project. The third author also acknowledges support by the Center for Nanophase Materials Sciences, sponsored by the Division of User Facilities, Basic Energy Sciences, U.S. Department of Energy.

Keywords

Backward SDEs
Jump diffusion processes
Material sciences
Nonlinear filtering problem

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10.4208/cicp.OA-2018-0238

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Lévy backward SDE filter for jump diffusion processes and its applications in material sciences

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