Approximation schemes for stochastic differential equations in Hilbert space

被引：3

作者：

Mishura, Yu. S. ^{[1
]}

Shevchenko, G. M. ^{[1
]}

机构：

[1] Kyi Taras Shevchenko Natl Univ, Dept Mech & Math, UA-01033 Kiev, Ukraine

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2007年 / 51卷 / 03期

关键词：

stochastic differential equations in Hilbert space; discrete-time approximations; Milstein scheme; Ito-Volterra type equation; EVOLUTION EQUATIONS; NUMERICAL APPROXIMATION; DRIVEN;

D O I：

10.1137/S0040585X97982487

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

For solutions of Ito - Volterra equations and semilinear evolution- type equations we consider approximations via the Milstein scheme, approximations by finite- dimensional processes, and approximations by solutions of stochastic differential equations ( SDEs) with bounded coefficients. We prove mean- square convergence for finite- dimensional approximations and establish results on the rate of mean- square convergence for two remaining types of approximation.

引用

页码：442 / 458

页数：17

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