Continuous-time random walk

In mathematics, a continuous-time random walk (CTRW) is a generalization of a stochastic jump process in which the jump lengths and jump times have predefined distributions.^[1]^[2]^[3]

Motivation

CTRW was introduced by Montroll and Weiss ^[4] as a generalization of physical diffusion process to effectively describe anomalous diffusion, i.e., the super- and sub-diffusive cases. An equivalent formulation of the CTRW is given by generalized master equations in the case of discrete jump lengths and fractional differential equations for the case where the process varies continuously. ^[5]

Examples

The Wiener process is the standard example of a continuous time random walk in which the waiting times are exponential and the jumps are continuous and normally distributed.

References

^ Klages, Rainer; Radons, Guenther; Sokolov, Igor M. Anomalous Transport: Foundations and Applications.
^ Paul, Wolfgang; Baschnagel, Jörg (2013-07-11). Stochastic Processes: From Physics to Finance. Springer Science & Business Media. pp. 72–. ISBN 9783319003276. Retrieved 25 July 2014.
^ Slanina, Frantisek (2013-12-05). Essentials of Econophysics Modelling. OUP Oxford. pp. 89–. ISBN 9780191009075. Retrieved 25 July 2014.
^ Elliott W. Montroll and George H. Weiss (1965). "Random Walks on Lattices. II". J. Math. Phys. 6: 167. doi:10.1063/1.1704269.
^ . M. Kenkre, E. W. Montroll, M. F. Shlesinger (1973). "Generalized master equations for continuous-time random walks". Journal of Statistical Physics. 9 (1): 45–50. doi:10.1007/BF01016796.{{cite journal}}: CS1 maint: multiple names: authors list (link)

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