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] The Wiener process is the standard example of a continuous time random walk.
Motivation
CTRW was introduced by Montroll and Weiss [4] as a generalization of physical diffusion process to effectively include the super- and sub-diffusive cases.[clarification needed] 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 continously.
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.
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