Effects of finite probing windows on the interpretation of the multifractal properties of random walks

¹  Consortium of the Americas for Interdisciplinary Science and Department of Physics and Astronomy University of New Mexico - Albuquerque NM 87131, USA
²  Instituto de Física, Universidade Federal de Alagoas - 57072-970, Maceió-AL, Brazil
³  Valles Caldera Trust, Jemez Springs - NM, 87025, USA
⁴  Department of Biology, University of New Mexico - Albuquerque, NM 87131, USA

Received: 9 October 2006
Accepted: 15 December 2006

Abstract

We investigate the general problem of how the finiteness of a probing window for measurements of the movements of a random walker can lead to spurious detection of multifractality as well as to incorrect values of Hurst exponents, and propose a method for correcting for these effects. We also study the case in which the roaming region of the walker is itself of limited extent, when a nonlinear interplay occurs between the roaming area and the window size. In the context of animal movements, we describe briefly an application of these ideas to mark-recapture observations in a mouse population, of interest to the important topic of the spread of the Hantavirus epidemic.