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Volume 10, Issue 4
Error Estimates of the Crank-Nicolson Scheme for Solving Backward Stochastic Differential Equations

W. Zhao, Y. Li & L. Ju

Int. J. Numer. Anal. Mod., 10 (2013), pp. 876-898.

Published online: 2013-10

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  • Abstract

In this paper, we study error estimates of a special $\theta$-scheme — the Crank-Nicolson scheme proposed in [25] for solving the backward stochastic differential equation with a general generator, $-dy_t = f(t, y_t, z_t)dt-z_tdW_t$. We rigorously prove that under some reasonable regularity conditions on $\varphi$ and $f$, this scheme is second-order accurate for solving both $y_t$ and $z_t$ when the errors are measured in the $L^p (p \geq 1)$ norm.

  • Keywords

Backward stochastic differential equations, Crank-Nicolson scheme, $\theta$-scheme, error estimate.

  • AMS Subject Headings

60H35, 60H10, 65C30

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-10-876, author = {}, title = {Error Estimates of the Crank-Nicolson Scheme for Solving Backward Stochastic Differential Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {4}, pages = {876--898}, abstract = {

In this paper, we study error estimates of a special $\theta$-scheme — the Crank-Nicolson scheme proposed in [25] for solving the backward stochastic differential equation with a general generator, $-dy_t = f(t, y_t, z_t)dt-z_tdW_t$. We rigorously prove that under some reasonable regularity conditions on $\varphi$ and $f$, this scheme is second-order accurate for solving both $y_t$ and $z_t$ when the errors are measured in the $L^p (p \geq 1)$ norm.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/601.html} }
TY - JOUR T1 - Error Estimates of the Crank-Nicolson Scheme for Solving Backward Stochastic Differential Equations JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 876 EP - 898 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/601.html KW - Backward stochastic differential equations, Crank-Nicolson scheme, $\theta$-scheme, error estimate. AB -

In this paper, we study error estimates of a special $\theta$-scheme — the Crank-Nicolson scheme proposed in [25] for solving the backward stochastic differential equation with a general generator, $-dy_t = f(t, y_t, z_t)dt-z_tdW_t$. We rigorously prove that under some reasonable regularity conditions on $\varphi$ and $f$, this scheme is second-order accurate for solving both $y_t$ and $z_t$ when the errors are measured in the $L^p (p \geq 1)$ norm.

W. Zhao, Y. Li & L. Ju. (1970). Error Estimates of the Crank-Nicolson Scheme for Solving Backward Stochastic Differential Equations. International Journal of Numerical Analysis and Modeling. 10 (4). 876-898. doi:
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