On a class of stochastic integro-differential equations

Abstract

The solutions of the stochastic integro-differential equation involving, in addition to the random transitions of the stochastic variable, a deterministic change, are obtained under various approximations. It is shown that the solution in the case of a negative deterministic change is strikingly different from the solution when the change is positive. Examples from physics and astro-physics are cited to illustrate such stochastic processes.