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

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.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002D-FE50-C Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002D-FE53-6
Genre: Journal Article

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Sim, A., Author
Liepe, J.1, Author              
Stumpf, M. P., Author
Affiliations:
1Research Group of Quantitative and System Biology, MPI for Biophysical Chemistry, Max Planck Society, ou_2466694              

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 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.

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Language(s): eng - English
 Dates: 2015-04-152015-04
 Publication Status: Published in print
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 Rev. Method: Peer
 Identifiers: DOI: 10.1103/PhysRevE.91.042115
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Title: Physical Review E
Source Genre: Journal
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Pages: 9 Volume / Issue: 91 (4) Sequence Number: 042115 Start / End Page: - Identifier: -