Kazuo Amano
Abstract:
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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