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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

A generalization of Mil'shtein's theorem for stochastic differential equations


Author: Georgiĭ Shevchenko
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 78 (2008).
Journal: Theor. Probability and Math. Statist. 78 (2009), 191-199
MSC (2000): Primary 60H10; Secondary 34G10, 47A50, 47D06
Published electronically: August 4, 2009
MathSciNet review: 2446859
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Abstract | References | Similar Articles | Additional Information

Abstract: A theorem on a relationship between local and global rates of convergence for a stochastic differential equation is proved in the paper. This theorem implies the convergence of Euler type approximations for semilinear evolution equations with a coercive operator in a Hilbert space.


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Additional Information

Georgiĭ Shevchenko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty of Mechanics and Mathematics, Kiev National Taras Shevchenko University, 64 Volodymyrska Street, 01033 Kiev, Ukraine
Email: zhora@univ.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-09-00772-8
PII: S 0094-9000(09)00772-8
Keywords: Stochastic differential equation, semilinear stochastic evolution equation, time {\discretisation }, Mil'shtein theorem
Received by editor(s): January 9, 2007
Published electronically: August 4, 2009
Article copyright: © Copyright 2009 American Mathematical Society