Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 03, pp. 1-8.

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

Author: Kazuo Amano (Gunma Univ., Kiryu, Japan)

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 04, 2012.
Math Subject Classifications: 60H10, 65C30.
Key Words: Newton's method; stochastic differential equation;
           second order error estimate.