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 continuously. [5]
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.
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