On stochastic integrodifferential equations via non-linear integral contractors. I
The authors study existence and uniqueness of an Itō-type integro-differential equation. In the classical theory of stochastic differential equations, the Lipschitz condition ensures existence and uniqueness of the solution. In this paper, the authors generalize the Lipschitz condition by introducing nonlinear bounded random integral contractors. For more details on random integral contractors see [\textit{M. Altman}, Contractors and contractor directions. Theory and applications. A new approach to solving equations. New York - Basel: Marcel Dekker (1977; Zbl 0363.65045); \textit{H.-H. Kuo}, J. Integral Equations 1, 35--46 (1979; Zbl 0455.35073)].
scientific article; zbMATH DE number 6217131