TITLE:
Numerical Approximation of Fractal Dimension of Gaussian Stochastic Processes
AUTHORS:
Freddy H. Marin Sanchez, William Eduardo Alfonso
KEYWORDS:
Stationary Gaussian Stochastic Processes, Fractal Dimension, Random Euler Numerical Scheme
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.12,
June
26,
2014
ABSTRACT:
In
this paper we propose a numerical method to estimate the fractal dimension of stationary
Gaussian stochastic processes using the random Euler numerical scheme and based
on an analytical formulation of the fractal dimension for filtered stochastic
signals. The discretization of continuous time processes through this random
scheme allows us to find, numerically, the expected value, variance and
correlation functions at any point of time. This alternative method for
estimating the fractal dimension is easy to implement and requires no
sophisticated routines. We use simulated data sets for stationary processes of
the type Random Ornstein Uhlenbeck to graphically illustrate the results and compare
them with those obtained whit the box counting theorem.