Journal of Applied Mathematics and Stochastic Analysis
Volume 7 (1994), Issue 1, Pages 25-31

The probabilistic approach to the analysis of the limiting behavior of an integro-diffebential equation depending on a small parameter, and its application to stochastic processes

O. V. Borisenko,1 A. D. Borisenko,2 and I. G. Malyshev3

1Kiev Polytechnic Institute, Department of Mathematics N3, Prospect Pobedy 3, Kiev 252056, Ukraine
2Kiev University, Department of Probability & Mathematical Statistics, Kiev 252017, Ukraine
3San Jose State University, Department of Mathematics & Computer Science, San Jose 95192, CA, USA

Received 1 December 1993; Revised 1 February 1994

Copyright © 1994 O. V. Borisenko et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Using connection between stochastic differential equation with Poisson measure term and its Kolmogorov's equation, we investigate the limiting behavior of the Cauchy problem solution of the integro differential equation with coefficients depending on a small parameter. We also study the dependence of the limiting equation on the order of the parameter.