2012/12/05 by Peter Straka, Straka, Peter
Decision Sciences · Environmental Science · Mathematics · Physics and Astronomy · #60B10 #60F17 #60G22 #60G50 #FOS: Mathematics #FOS: Physical sciences #Fuzzy Systems and Optimization #Groundwater flow and contamination studies #Probabilistic and Robust Engineering Design #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #math.PR #msc:60B10 #msc:60F17 #msc:60G22 #msc:60G50
paper · pdf · doi:10.48550/arxiv.1212.1197
Results have been merged with other article, and hence this article is withdrawn
openalex publication_date 2012/12/05 · arxiv created 2015/01/03 · arxiv updated 2015/01/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Continuous Time Random Walks (CTRWs) are jump processes with random waiting times between jumps. We study scaling limits for CTRWs where the distribution of jumps and waiting times is coupled and varies in space and time. Such processes model e.g. anomalous diffusion processes in a space- and time-dependent potential. Conditions for the process-convergence of CTRWs are given, and the limits are characterised by four coefficients. Kolmogorov forwards and backwards equations with non-local time operators are derived, and three models for anomalous diffusion are presented: i) Subdiffusion in a time-dependent potential, ii) subdiffusion with spatially varying waiting times and iii) Lévy walks with space- and time-dependent drift.