Convergence in (2m)-{\rm th} mean for perturbed stochastic integrodifferential equations

Svetlana Jankovi\'c and Miljana Jovanovi\'c

Abstract: 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 integro-differential 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

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