On a stochastic integral equation of the Volterra type

In a very general sense, random or stochastic integral equations arise in such diverse areas as the physical, biological, oceanographic and engineering sciences. The manner in which such equations arise and their importance to various physical phenomena have been investigated by many scientists [1]; however, not until quite recently have attempts been made to develop and unify the theory of stochastic integral equations. The objective of this investigation is the study of a specific class of stochastic integral equations of Volterra type, which seems to be the most general form considered to date. Specifically, we consider a stochastic integral equation of Volterra type of the form