%0 Journal Article
%T Newton's method for stochastic differential equations and its probabilistic second-order error estimate
%A Kazuo Amano
%J Electronic Journal of Differential Equations
%D 2012
%I Texas State University
%X 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.
%K Newton's method
%K stochastic differential equation
%K second order error estimate
%U http://ejde.math.txstate.edu/Volumes/2012/03/abstr.html