Non-Independent Continuous Time Random Walks

24 Pages Posted: 1 Aug 2007

See all articles by Miquel Montero

Miquel Montero

University of Barcelona - Departament de Física de la Matèria Condensada

Jaume Masoliver

University of Barcelona - Department of Physics

Date Written: July 27, 2007

Abstract

The usual development of the continuous time random walk (CTRW) assumes that jumps and time intervals are independent (and identically distributed) random variables. In this paper we address the theoretical setting of non-independent CTRW's where jumps and/or time intervals are correlated. An exact solution to the problem is obtained for the special but relevant case in which the correlation solely depends on the signs of consecutive jumps. Even in this simple case some interesting features arise such as transitions from unimodal to bimodal distributions due to correlation. We also develop the necessary analytical techniques and approximations to handle more general situations that can appear in practice.

Keywords: Stochastic processes, Markov processes, Random walks, CTRW, Approximations

Suggested Citation

Montero, Miquel and Masoliver, Jaume, Non-Independent Continuous Time Random Walks (July 27, 2007). Available at SSRN: https://ssrn.com/abstract=1003796 or http://dx.doi.org/10.2139/ssrn.1003796

Miquel Montero (Contact Author)

University of Barcelona - Departament de Física de la Matèria Condensada ( email )

Martí i Franquès, 1
Barcelona, Catalonia 08028
Spain
+34 93 403 92 53 (Phone)
+34 93 402 11 55 (Fax)

Jaume Masoliver

University of Barcelona - Department of Physics ( email )

Barcelona, E-08028
Spain
00 34 3 402 11 59 (Phone)
00 34 3 402 11 49 (Fax)

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