Existence and Uniqueness Theorem of Fuzzy Stochastic  Ordinary Differential Equations

Nabaa R. Kareem; Fadhel S. Fadhel; Sadiq Al-Nassir

doi:10.24996/ijs.2023.64.11.33

Authors

Nabaa R. Kareem Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Fadhel S. Fadhel Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Jadriya, Baghdad, Iraq
Sadiq Al-Nassir Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2023.64.11.33

Keywords:

Existence and uniqueness theorem, Fuzzy differential equations, Stochastic differential equations, Brownian motion

Abstract

A fuzzy valued diffusion term, which in a fuzzy stochastic differential equation refers to one-dimensional Brownian motion, is defined by the meaning of the stochastic integral of a fuzzy process. In this paper, the existence and uniqueness theorem of fuzzy stochastic ordinary differential equations, based on the mean square convergence of the mathematical induction approximations to the associated stochastic integral equation, are stated and demonstrated.