Simulation of Multifractional Brownian Motion

. Multifractional Brownian motion (MFBm) is a generalization of Fractional Brownian motion (FBm) in which the Hurst parameter varies with time in a prescribed manner. In this paper we investigate an approximate method for simulating realizations of MFBm on a finite grid. Keywords. Fractal dimension; Hurst parameter; kriging; long-range dependence; sample path roughness; stationary increments. 1 Introduction 1.1 Review of FBm FBm is a zero-mean self-similar Gaussian process fBH (t)g t0 with covariance function given by cov fBH (s); BH (t)g = 1 2 n jsj 2H + jtj 2H \Gamma js \Gamma tj 2H o (1) where H 2 (0; 1) is known as the Hurst parameter. Note that BH (0) j 0 and varfBH (t)g = t 2H . In the special case H = 1=2, FBm reduces to ordinary Brownian motion. An important property of FBm, which follows from (1), is that it has stationary increments. FBm has proved to be of considerable interest in diverse fields such as Hydrology, Signal Processing and Financial Mathematics. B..