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March 2009 A note on Newton’s method for stochastic differential equations and its error estimate
Kazuo Amano
Proc. Japan Acad. Ser. A Math. Sci. 85(3): 19-21 (March 2009). DOI: 10.3792/pjaa.85.19

Abstract

Kawabata and Yamada [3] proposed an implicit Newton method for stochastic differential equations and proved its convergence. They proved an error estimate in a sufficiently small time interval and extended it to a global convergence theorem by using open-closed method. In this note, the author gives an explicit Newton scheme which is equivalent to Kawabata-Yamada’s implicit formulation (Remark 1) and prove its direct error estimate (Theorem 2.1). His result could provide a key to solve the open problem of second order convergence (see Remark of Theorem 2.1 and [2]).

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Kazuo Amano. "A note on Newton’s method for stochastic differential equations and its error estimate." Proc. Japan Acad. Ser. A Math. Sci. 85 (3) 19 - 21, March 2009. https://doi.org/10.3792/pjaa.85.19

Information

Published: March 2009
First available in Project Euclid: 2 March 2009

zbMATH: 1171.60012
MathSciNet: MR2502413
Digital Object Identifier: 10.3792/pjaa.85.19

Subjects:
Primary: 60H10 , 60H35

Keywords: error estimate , Newton’s method for stochastic differential equations

Rights: Copyright © 2009 The Japan Academy

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Vol.85 • No. 3 • March 2009
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