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Title: Continuous-Time Modeling of Random Searches: Statistical Properties and Inference
Authors: Kawai, Reiichiro
First Published: 23-May-2012
Citation: Journal of Physics A: Mathematical and Theoretical, 2012, 45 (23), 5004.
Abstract: Mathematical modeling of random searches is of great relevance in the fields of physics, chemistry, biology or modern ecology. A large number of existing studies record the search movement at equidistant time intervals and model such time series data directly with discrete-time random walks, such as Lévy flights and correlated random walks. Given the increasing availability of high-resolution observation data, statistical inference for search paths based on such high-resolution data has recently become one of the major interests and has raised an important issue of robustness of random walk models to the sampling rate, as estimation results for the discrete observation data are found to be largely different at different sampling rates even when the underlying movement is supposedly independent of scale. To address this issue, in this paper, we propose to model the continuous-time search paths directly with a continuous-time stochastic process for which the observer makes statistical inference based on its discrete observation. As continuous-time counterparts of Lévy flights, we consider two-dimensional Lévy processes and discuss the relevance of those models based upon advantages and limitations in terms of statistical properties and inference. Among the proposed models, the Brownian motion is most tractable in various ways while its Gaussianity and infinite variation of sample paths do not well describe the reality. Such drawbacks in statistical properties may be remedied by employing the stable and tempered stable Lévy motions, while those models are less tractable and cause an issue in statistical inference.
DOI Link: 10.1088/1751-8113/45/23/235004
ISSN: 1751-8113
eISSN: 1751-8121
Version: Post print
Peer reviewed
Type: Journal Article
Rights: © 2012 IOP Publishing Ltd. Deposited with reference to the publisher's archiving policy available from the SHERPA/RoMEO website. This is an author-created, uncopyedited version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretical. IOP Publishing is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher-authenticated version is available online at
Appears in Collections:Published Articles, Dept. of Mathematics

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