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

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

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...

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Bibliographic Details
Main Author: Kazuo Amano
Format: Article
Language:English
Published: Texas State University 2012-01-01
Series:Electronic Journal of Differential Equations
Subjects:
Newton's method
stochastic differential equation
second order error estimate
Online Access:http://ejde.math.txstate.edu/Volumes/2012/03/abstr.html
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spelling doaj-9a795aa80d80490ca9123f9fdca8b5e22020-11-24T22:46:32ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912012-01-01201203,18Newton's method for stochastic differential equations and its probabilistic second-order error estimateKazuo AmanoKawabata 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. http://ejde.math.txstate.edu/Volumes/2012/03/abstr.htmlNewton's methodstochastic differential equationsecond order error estimate
collection DOAJ
language English
format Article
sources DOAJ
author Kazuo Amano
spellingShingle Kazuo Amano
Newton's method for stochastic differential equations and its probabilistic second-order error estimate
Electronic Journal of Differential Equations
Newton's method
stochastic differential equation
second order error estimate
author_facet Kazuo Amano
author_sort Kazuo Amano
title Newton's method for stochastic differential equations and its probabilistic second-order error estimate
title_short Newton's method for stochastic differential equations and its probabilistic second-order error estimate
title_full Newton's method for stochastic differential equations and its probabilistic second-order error estimate
title_fullStr Newton's method for stochastic differential equations and its probabilistic second-order error estimate
title_full_unstemmed Newton's method for stochastic differential equations and its probabilistic second-order error estimate
title_sort newton's method for stochastic differential equations and its probabilistic second-order error estimate
publisher Texas State University
series Electronic Journal of Differential Equations
issn 1072-6691
publishDate 2012-01-01
description 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.
topic Newton's method
stochastic differential equation
second order error estimate
url http://ejde.math.txstate.edu/Volumes/2012/03/abstr.html
work_keys_str_mv AT kazuoamano newtonsmethodforstochasticdifferentialequationsanditsprobabilisticsecondordererrorestimate
_version_ 1725684929745911808

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