2007/07/31 by Miquel Montero, Jaume Masoliver · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Diffusion and Search Dynamics #Nonlinear Dynamics and Pattern Formation #physics.data-an
paper · pdf · doi:10.1103/physreve.76.061115
published as PHYSICAL REVIEW E 76, 061115 (2007) · revtex4, preprint, aps, 25 pages, 8 plots in 2 figures, submitted for publication; revised version, references changed and expanded
arxiv created 2007/09/21 · openalex publication_date 2007/12/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The usual development of the continuous-time random walk (CTRW) assumes that jumps and time intervals are a two-dimensional set of independent and identically distributed random variables. In this paper, we address the theoretical setting of nonindependent CTRWs where consecutive 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.