Numerical Solution of Fuzzy Stochastic Differential Equation

TL;DR

This paper introduces a novel method for solving fuzzy stochastic differential equations by integrating fuzzy arithmetic with traditional stochastic techniques, enabling handling of uncertainty in system parameters.

Contribution

It presents an alternative approach using fuzzy arithmetic to solve FSDEs, including exact and Euler-Maruyama methods with fuzzy parameters.

Findings

Successful application to standard SDEs

Demonstration of fuzzy Euler-Maruyama approximation

Handling of uncertain parameters in stochastic systems

Abstract

In this paper an alternative approach to solve uncertain Stochastic Differential Equation (SDE) is proposed. This uncertainty occurs due to the involved parameters in system and these are considered as Triangular Fuzzy Numbers (TFN). Here the proposed fuzzy arithmetic in [2] is used as a tool to handle Fuzzy Stochastic Differential Equation (FSDE). In particular, a system of Ito stochastic differential equations is analysed with fuzzy parameters. Further exact and Euler Maruyama approximation methods with fuzzy values are demonstrated and solved some standard SDE.