Geodesic
Newton's method for stochastic differential equations and its probabilistic second-order error estimate
Electronic journal of differential equations, Tome 2012 (2012)
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.
Classification : 60H10, 65C30
Keywords: Newton's method, stochastic differential equation, second order error estimate 
@article{EJDE_2012__2012__a35,
     author = {Amano,  Kazuo},
     title = {Newton's method for stochastic differential equations and its probabilistic second-order error estimate},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1239.60044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a35/}
}
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JO  - Electronic journal of differential equations
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VL  - 2012
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ID  - EJDE_2012__2012__a35
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%0 Journal Article
%A Amano,  Kazuo
%T Newton's method for stochastic differential equations and its probabilistic second-order error estimate
%J Electronic journal of differential equations
%D 2012
%V 2012
%U http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a35/
%G en
%F EJDE_2012__2012__a35
Amano,  Kazuo. Newton's method for stochastic differential equations and its probabilistic second-order error estimate. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a35/