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Volume 27, Issue 2
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

Commun. Comput. Phys., 27 (2020), pp. 589-618.

Published online: 2019-12

[An open-access article; the PDF is free to any online user.]

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65C30, 65K10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

bao@math.fsu.edu (Feng Bao)

archibaldrk@ornl.gov (Richard Archibald)

maksymovychp@ornl.gov (Peter Maksymovych)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-589, author = {Bao , FengArchibald , Richard and Maksymovych , Peter}, title = {Lévy Backward SDE Filter for Jump Diffusion Processes and Its Applications in Material Sciences}, journal = {Communications in Computational Physics}, year = {2019}, volume = {27}, number = {2}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0238}, url = {http://global-sci.org/intro/article_detail/cicp/13460.html} }
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 -

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.

Bao , FengArchibald , Richard and Maksymovych , Peter. (2019). Lévy Backward SDE Filter for Jump Diffusion Processes and Its Applications in Material Sciences. Communications in Computational Physics. 27 (2). 589-618. doi:10.4208/cicp.OA-2018-0238
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