Electron. J. Diff. Equ., Vol. 2012 (2012), No. 03, pp. 1-8.

Newton's method for stochastic differential equations and its probabilistic second-order error estimate

Kazuo Amano

Kawabata and Yamada [5] proposed an implicit Newton's method for nonlinear stochastic differential equations and proved its convergence. Later Amano [2] gave an explicit formulation of method and showed its direct error estimate. In this article, we prove a probabilistic second-order error estimate which has been an open problem since 1991.

Submitted June 27, 2011. Published January 4, 2012.
Math Subject Classifications: 60H10, 65C30.
Key Words: Newton's method; stochastic differential equation; second order error estimate.

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Kazuo Amano
Department of Mathematics
Faculty of Engineering, Gunma University
Kiryu, 376-8515, Japan
email: kamano@gunma-u.ac.jp

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