Geodesic
Newton's method for stochastic differential equations and its probabilistic second-order error estimate
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a35/}
}
TY  - JOUR
AU  - Amano, Kazuo
TI  - Newton's method for stochastic differential equations and its probabilistic second-order error estimate
JO  - Electronic Journal of Differential Equations
PY  - 2012
VL  - 2012
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a35/
LA  - en
ID  - EJDE_2012__2012__a35
ER  - 
%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
%I mathdoc
%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/