Year: 2013
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-IJNAM-601
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 4 : pp. 876–898
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Backward stochastic differential equations Crank-Nicolson scheme $\theta$-scheme error estimate.