Journal article

Goldstein-Kac telegraph processes with random speeds: Path probabilities, likelihoods, and reported Lévy flights.

Aaron Sim, Juliane Liepe, Michael PH Stumpf

Phys Rev E Stat Nonlin Soft Matter Phys | Published : 2015

Abstract

The Goldstein-Kac telegraph process describes the one-dimensional motion of particles with constant speed undergoing random changes in direction. Despite its resemblance to numerous real-world phenomena, the singular nature of the resultant spatial distribution of each particle precludes the possibility of any a posteriori empirical validation of this random-walk model from data. Here we show that by simply allowing for random speeds, the ballistic terms are regularized and that the diffusion component can be well-approximated via the unscented transform. The result is a computationally efficient yet robust evaluation of the full particle path probabilities and, hence, the parameter likeliho..

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University of Melbourne Researchers

Grants

Awarded by National Centre for the Replacement, Refinement and Reduction of Animals in Research