Existence and uniqueness for solutions to fuzzy stochastic differential equations driven by local martingales under the non-Lipschitzian condition

This paper makes a research into a class of fuzzy stochastic differential equations (FSDEs) driven by a continuous local martingale under the non-Lipschitzian condition. Such equations can be useful in modelling of hybrid systems, where the phenomena are subjected to two kinds of uncertainties: randomness and fuzziness, simultaneously. The solutions of FSDEs are the fuzzy stochastic processes, and their uniqueness is considered to be in a strong sense. Thus, the existence and uniqueness of solutions to FSDEs under the non-Lipschitzian condition is first proven. And the continuity of solutions to FSDEs with respect to the initial data or the coefficients of the equations is investigated.