Numerical Solution of Fuzzy Stochastic Differential Equation
This addresses uncertainty in stochastic systems for fields like engineering and finance, but it is incremental as it applies existing fuzzy arithmetic to known methods.
The paper tackles solving stochastic differential equations with uncertain parameters modeled as triangular fuzzy numbers, proposing an approach that uses fuzzy arithmetic and demonstrates exact and Euler-Maruyama approximation methods on standard SDEs.
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.