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Splitting scheme for backward doubly stochastic differential equations

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Abstract

A splitting scheme is proposed for a class of backward doubly stochastic differential equations (BDSDEs). The main idea is to decompose the backward doubly stochastic differential equation into a backward stochastic differential equation and a stochastic differential equation, which are much easier to solve than the BDSDE itself. The two equations are then approximated by first-order finite difference schemes, which results in a first-order scheme for the backward doubly stochastic differential equation. Numerical experiments are conducted to illustrate the convergence rate of the proposed scheme.

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Funding

This research is partially supported by the NSFC (grant numbers 12201242 and 12071175), the US Department of Energy through FASTMath Institute and Office of Science, Advanced Scientific Computing Research program under the grant DE-SC0022297, and the US Department of Energy’s Advanced Scientific Computing Research program under the grant DE-SC0022253. The author would also like to acknowledge the support from the US National Science Foundation through project DMS-2142672.

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Authors and Affiliations

  1. Department of Mathematics, Florida State University, 1017 Academic Way, Tallahassee, 32304, FL, USA

    Feng Bao

  2. Department of Mathematics, Auburn University, Auburn, 36849, AL, USA

    Yanzhao Cao

  3. School of Mathematics, Jilin University, Changchun, Jilin, 130012, China

    He Zhang

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  1. Feng Bao
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  2. Yanzhao Cao
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  3. He Zhang
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Correspondence to Yanzhao Cao.

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Communicated by: Yuesheng Xu

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Bao, F., Cao, Y. & Zhang, H. Splitting scheme for backward doubly stochastic differential equations. Adv Comput Math 49, 65 (2023). https://doi.org/10.1007/s10444-023-10053-z

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  • DOI: https://doi.org/10.1007/s10444-023-10053-z

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