Stochastic integrals and stochastic equations in set-valued and fuzzy-valued frameworks

In this paper, we study the existence, uniqueness and properties of solutions to set-valued and fuzzy-valued stochastic differential equations with respect to finite variation and martingale integrators. We present new types of such equations that generalize those studied earlier. For this aim we introduce properly defined new types of stochastic integrals in set-valued and fuzzy-valued settings and we establish their main properties. The results obtained in the paper generalize conclusions dealing with this topic known both in deterministic and stochastic cases.