On random solutions of Volterra-Fredholm integral equations
Existence, uniqueness and boundedness theorems for solutions of the nonlinear stochastic integral equation \[ x(t;\omega)=f(t;\omega)+\int^{t}_{0}a(t,s;\omega)g(s,x(s;\omega))ds+\i nt^{\infty}_{0}b(t,s;\omega)h(s,x(s;\omega))ds,\quad t\geq 0 \] are obtained using the admissibility theory of integral operators and contractor theory. Two additional boundedness results are proved in case g(t,x) and h(t,x) are independent of t and these results are illustrated by examples where \(b(t,s;\omega)\equiv 0\) and \(a(t,s;\omega)=a(t- s;\omega).\)
scientific article; zbMATH DE number 3848345