<title>Data-driven differential equation modeling of fBm processes</title>

Abstract

This paper presents a unique method for modeling fractional Brownian motion type data sets with ordinary differential equations (ODE) and a unique <b>fractal operator</b>. To achieve such modeling, a new method is introduced using Turlington polynomials to obtain continuous and differentiable functions. These functions are then fractal interpolated to yield fine structure. Spectral decomposition is used to obtain a differential equation model which is then fractal interpolated to forecast a fBm trajectory. This paper presents an overview of the theory and our modeling approach along with example results.