Properties of fuzzy Ito integrals with respect to fuzzy Brownian motion

Abstract

Integral of a stochastic process with respect to Brownian motion is called Ito integral. Here the stochastic process and Brownian motion are random as well as fuzzy. Hence the Ito integral is fuzzy Ito integral. This paper deals with the properties of fuzzy Ito integral for simple adapted process with respect to fuzzy Brownian motion. The quadratic variance and covariance of FII are discussed. The concept of fuzzy simple adapted process, fuzzy martingale, fuzzy functions are used to derive the properties of fuzzy Ito integrals.