Approximation schemes for fuzzy stochastic integral equations

摘要

We consider fuzzy stochastic integral equations with stochastic Lebesgue trajectory integrals and fuzzy stochastic Itô trajectory integrals. Some methods of construction of approximate solutions to such the equations are examined. We study the Picard type approximations, the Carathéodory type approximations and the Maruyama type approximations of solutions. In considered framework, the solutions and approximate solutions are mappings with values in the space of fuzzy sets with basis of square integrable random vectors. Under Lipschitz and linear growth conditions each sequence of considered approximate solutions converges to the exact unique solution of the given fuzzy stochastic integral equation. For each type of approximate solutions, we show that the sequence of approximations is uniformly bounded and obtain some bounds for a distance between nth approximation and exact solution.