Symmetric Fuzzy Stochastic Differential Equations with Generalized Global Lipschitz Condition

Abstract

The paper contains a discussion on solutions to symmetric type of fuzzy stochastic differential equations. The symmetric equations under study have drift and diffusion terms symmetrically on both sides of equations. We claim that such symmetric equations have unique solutions in the case that equations’ coefficients satisfy a certain generalized Lipschitz condition. To show this, we prove that an approximation sequence converges to the solution. Then, a study on stability of solution is given. Some inferences for symmetric set-valued stochastic differential equations end the paper.

Keywords

• symmetric fuzzy stochastic differential equation
• symmetric set-valued stochastic differential equations
• existence and uniqueness of solution
• successive approximations
• stability of solution
• fuzziness