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Theory of Probability and Mathematical Statistics

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Rate of convergence of discrete approximate solutions of stochastic differential equations in a Hilbert space


Author: G. Shevchenko
Translated by: The author
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 69 (2003).
Journal: Theor. Probability and Math. Statist. 69 (2004), 187-199
MSC (2000): Primary 60H35; Secondary 60H10, 60H20, 65C30
DOI: https://doi.org/10.1090/S0094-9000-05-00625-3
Published electronically: February 9, 2005
MathSciNet review: 2110916
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider discrete-time approximations for stochastic differential equations in a Hilbert space. The rate of convergence of approximations is established for equations with Lipschitz continuous coefficients and for semilinear evolution type equations with an unbounded drift. As an auxiliary result, the rate of convergence of approximations is obtained for Itô-Volterra equations in a Hilbert space.


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Additional Information

G. Shevchenko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty of Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: zhora@univ.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-05-00625-3
Keywords: Stochastic differential equations in a Hilbert space, discrete-time approximations, equations of the It\^o--Volterra type
Received by editor(s): December 16, 2002
Published electronically: February 9, 2005
Article copyright: © Copyright 2005 American Mathematical Society

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