Data-driven differential equation modeling of fBm processes

Holger M. Jaenisch; James W. Handley; Jeffery P. Faucheux

doi:10.1117/12.502479

5 January 2004 Data-driven differential equation modeling of fBm processes

Holger M. Jaenisch, James W. Handley, Jeffery P. Faucheux

Proceedings Volume 5204, Signal and Data Processing of Small Targets 2003; (2004) https://doi.org/10.1117/12.502479
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

This paper presents a unique method for modeling fractional Brownian motion type data sets with ordinary differential equations (ODE) and a unique fractal operator. 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.

Citation Download Citation

Holger M. Jaenisch, James W. Handley, and Jeffery P. Faucheux "Data-driven differential equation modeling of fBm processes", Proc. SPIE 5204, Signal and Data Processing of Small Targets 2003, (5 January 2004); https://doi.org/10.1117/12.502479

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