stochastic functional differential equations distributed memory term numerical methods strong approximations The $\Theta$-Maruyama scheme for stochastic
functional differential equations with distributed memory term
Evelyn Buckwar Buckwar
Evelyn
Institut für Mathematik,
Humboldt-Universität zu Berlin (ISSN 0863-0976), 13
The $\Theta$-Maruyama scheme for stochastic functional differential
equations with distributed memory term
Evelyn Buckwar
Preprint series: Institut für Mathematik,
Humboldt-Universität zu Berlin (ISSN 0863-0976), 13
MSC 2000
- 65C30 Stochastic differential and integral equations
- 60H35 Computational methods for stochastic equations
Abstract
We
consider the problem of strong approximations of the solution of
It\^{o} stochastic functional differential equations involving a
distributed delay term. The mean-square consistency of a class of
schemes, the $\Theta$-Maruyama methods, is analysed, using an
appropriate It{\^o}-formula. In particular, we investigate the
consequences of the choice of a quadrature formula. Numerical examples
illustrate the theoretical results.
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