Electron. J. Diff. Equ.,
Vol. 2012 (2012), No. 03, pp. 18.
Newton's method for stochastic differential equations and its
probabilistic secondorder error estimate
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 secondorder 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.
Show me the PDF file (183 KB),
TEX file, and other files for this article.

Kazuo Amano
Department of Mathematics
Faculty of Engineering,
Gunma University
Kiryu, 3768515, Japan
email: kamano@gunmau.ac.jp

Return to the EJDE web page