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Perturbed stochastic hereditary differential equations with integral contractors

✍ Scribed by S. Janković; M. Jovanović

Book ID
104352214
Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
537 KB
Volume
42
Category
Article
ISSN
0898-1221

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✦ Synopsis

The present paper deals with the asymptotic behavior of the solution of the perturbed stochastic hereditary differential equation of the Ito type, by comparing it in the (2m) th moment sense with the solution of the appropriate unperturbed equation, on finite intervals or on intervals whose length tends to infinity. The problems are considered by using the concept of a random integral contractor, which includes the Lipschitz condition as a special case. (~) 2001 Elsevier Science Ltd. All rights reserved. Keywords--Stochastic hereditary differential equation, "Small" perturbations, Random integral contractor, Closeness in the (2m) th mean.

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## Abstract This paper is devoted to the large class of stochastic differential equations of the Ito type whose coefficients are functionally perturbed and depend on a small parameter. The solution of a such equation is compared with the solution of the corresponding unperturbed equation, in the (2