Fuzzy and Set-Valued Stochastic Differential Equations With Local Lipschitz Condition


We tend to are involved with the fuzzy stochastic differential equations driven by multidimensional Brownian motion viewed as a tool used to describe the behavior of dynamic systems operating in fuzzy environments with stochastic noises. Beneath the uniform Lipschitz condition, we prove the native uniqueness theorem for the solutions of fuzzy stochastic differential equations. Next we have a tendency to show, assuming the Lipschitz condition is glad only regionally, that these equations have a distinctive answer. The actual fact that the solution is bounded is additionally proved. We have a tendency to conclude the paper with a range of corresponding results holding for the deterministic fuzzy differential equations and set-valued stochastic differential equations with native Lipschitz condition.

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