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Volume 41, Issue 2
Two-Step Scheme for Backward Stochastic Differential Equations

Qiang Han & Shaolin Ji

DOI: 10.4208/jcm.2112-m2019-0289

J. Comp. Math., 41 (2023), pp. 287-304.

Published online: 2022-11

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  • Abstract

In this paper, a stochastic linear two-step scheme has been presented to approximate backward stochastic differential equations (BSDEs). A necessary and sufficient condition is given to judge the $\mathbb{L}_2$-stability of our numerical schemes. This stochastic linear two-step method possesses a family of $3$-order convergence schemes in the sense of strong stability. The coefficients in the numerical methods are inferred based on the constraints of strong stability and $n$-order accuracy ($n\in\mathbb{N}^+$). Numerical experiments illustrate that the scheme is an efficient probabilistic numerical method.

  • Keywords

Backward stochastic differential equation, Stochastic linear two-step scheme, Local truncation error, Stability and convergence.

  • AMS Subject Headings

60H35, 60H10, 65C05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

201411272@mail.sdu.edu.cn (Qiang Han)

jsl@sdu.edu.cn (Shaolin Ji)

  • BibTex
  • RIS
  • TXT
@Article{JCM-41-287, author = {Han , Qiang and Ji , Shaolin}, title = {Two-Step Scheme for Backward Stochastic Differential Equations}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {41}, number = {2}, pages = {287--304}, abstract = {

In this paper, a stochastic linear two-step scheme has been presented to approximate backward stochastic differential equations (BSDEs). A necessary and sufficient condition is given to judge the $\mathbb{L}_2$-stability of our numerical schemes. This stochastic linear two-step method possesses a family of $3$-order convergence schemes in the sense of strong stability. The coefficients in the numerical methods are inferred based on the constraints of strong stability and $n$-order accuracy ($n\in\mathbb{N}^+$). Numerical experiments illustrate that the scheme is an efficient probabilistic numerical method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2112-m2019-0289}, url = {http://global-sci.org/intro/article_detail/jcm/21181.html} }
TY - JOUR T1 - Two-Step Scheme for Backward Stochastic Differential Equations AU - Han , Qiang AU - Ji , Shaolin JO - Journal of Computational Mathematics VL - 2 SP - 287 EP - 304 PY - 2022 DA - 2022/11 SN - 41 DO - http://doi.org/10.4208/jcm.2112-m2019-0289 UR - https://global-sci.org/intro/article_detail/jcm/21181.html KW - Backward stochastic differential equation, Stochastic linear two-step scheme, Local truncation error, Stability and convergence. AB -

In this paper, a stochastic linear two-step scheme has been presented to approximate backward stochastic differential equations (BSDEs). A necessary and sufficient condition is given to judge the $\mathbb{L}_2$-stability of our numerical schemes. This stochastic linear two-step method possesses a family of $3$-order convergence schemes in the sense of strong stability. The coefficients in the numerical methods are inferred based on the constraints of strong stability and $n$-order accuracy ($n\in\mathbb{N}^+$). Numerical experiments illustrate that the scheme is an efficient probabilistic numerical method.

Han , Qiang and Ji , Shaolin. (2022). Two-Step Scheme for Backward Stochastic Differential Equations. Journal of Computational Mathematics. 41 (2). 287-304. doi:10.4208/jcm.2112-m2019-0289
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