Numerical solution of Langevin stochastic differential equation with uncertain parameters

Abstract

Abstract Stochastic differential equations (SDEs) with impreciseness and vagueness form uncertain stochastic differential equations (SDE), which may be the more generalized differential equation for handling uncertainties. In this chapter, two different approaches for solving uncertain stochastic differential equations (SDE) are discussed. Uncertainties are taken in the initial conditions as well as the associated parameters in terms of triangular fuzzy numbers (TFN). The limit method for fuzzy arithmetic has been used as a tool to handle the fuzzy stochastic differential equation (FSDE). In particular, a system of Ito SDEs has been analyzed with fuzzy parameters. Further, the fuzzy Euler-Maruyama method (FEMM) and fuzzy Milstein method (FMM) are demonstrated through an example problem for different cases.