Numerical Approximation of Fractal Dimension of Gaussian Stochastic Processes  

作　　者：Freddy H. Marin Sanchez William Eduardo Alfonso 

机构地区：[1]Basic Science Department, EAFIT University, Carrera 49 # 7 Sur-50, Medellín, Colombia

出　　处：《Applied Mathematics》2014年第12期1763-1772,共10页应用数学（英文）

摘　　要：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.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.

关 键 词：STATIONARY GAUSSIAN Stochastic Processes FRACTAL DIMENSION RANDOM EULER Numerical Scheme 

分 类 号：O1[理学—数学]