One presents a survey of the investigations in the theory of Volterra integral equations, reviewed in Ref. Zh. “Mat.” between 1966–1976.

Volterra integral equations

We establish sufficient conditions for the existence and
uniqueness of random solutions of nonlinear Volterra-Fredholm stochastic integral
equations of mixed type by using admissibility theory and fixed point theorems. The
results obtained in this paper generalize the results of several papers.

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Existence of Solutions of Nonlinear Stochastic Volterra Fredholm Integral Equations of Mixed Type

The aim of the present paper is to study a non-linear perturbed integral equation of the form for t⩾0 and ωϵΩ the supporting set of the probability measure space (Omega;, F, P). Sufficiant conditions are given for the existence and uniqueness of a random solution, a. mean square continuous stochastic process, and the stability behaviour of the system. Stability in the mean, almost surely stable, and exponentially stable; in the moan of the above system are studied.

Ronald A. Tourgee

Papers

Existence and stability behaviour of a non-linear perturbed stochastic system