Random integral equation

Summary

A random integral equation is an integral equation whose kernel, forcing term or both depend on a random parameter. For each outcome of the randomness one gets an ordinary integral equation, and the solution is a stochastic process. The basic questions are existence, uniqueness and measurability of such random solutions, and the laws of the solutions. Such equations model systems with uncertain coefficients, such as materials with random properties. They differ from stochastic integral equations with Itô integrals, where the integral against a Wiener process is not defined path by path.