Integro-differential equations for the characteristic functional that are generated by a system of random integral equations (Q1007030)

The paper deals with a boundary value problem for a system of integro-differential equations with variational derivatives. Variational derivatives of characteristic functionals are widely used for various purposes in the theory of random processes. The authors derive the relationship between the considered problem and a coupled system of integral equations with a power-law nonlinearity whose kernels and right-hand sides are random functions. Special cases and examples are also considered.