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

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Liepe,  J.
Research Group of Quantitative and System Biology, MPI for Biophysical Chemistry, Max Planck Society;

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Citation

Sim, A., Liepe, J., & Stumpf, M. P. (2015). Goldstein-Kac telegraph processes with random speeds: Path probabilities, likelihoods, and reported Lévy flights. Physical Review E, 91(4): 042115. doi:10.1103/PhysRevE.91.042115.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002D-FE50-C
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 likelihoods of this generalized telegraph process. We demonstrate how a population diffusing under such a model can lead to non-Gaussian asymptotic spatial distributions, thereby mimicking the behavior of an ensemble of Lévy walkers.