PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 68(82), pp. 133144 (2000) 

Convergence in (2m){\rm th} mean for perturbed stochastic integrodifferential equationsSvetlana Jankovi\'c and Miljana Jovanovi\'cFilozofski fakultet, Nis, YugoslaviaAbstract: Our goal is to study the (2m)th asymptotic behavior for the family of stochastic processes $x^{\varepsilon}=(x_t^{\varepsilon}$, $t\in [t_0,\infty))$, depending on a ``small'' parameter $\varepsilon\in (0,1)$. We consider the case when $x^{\varepsilon}$ is the solution of an Itô's stohastic integrodifferential equation whose coefficients are additionally perturbed. We compare the solution $x^{\varepsilon}$ with the solution of an appropriate unperturbed equation of the equal type. Sufficient conditions under which these solutions are close in the $(2m)$th moment sense on intervals whose length tends to infinity are given. Classification (MSC2000): 60H10 Full text of the article:
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© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
