Continuous time persistent random walk: a review and some generalizations*
1 Department of Condensed Matter Physics and Complex Systems Institute (UBICS), University of Barcelona, Catalonia, Spain
2 Department of Chemistry and Biochemistry and BioCircuits Institute, University of California, San Diego, USA
Received: 1 March 2017
Received in final form: 28 March 2017
Published online: 14 June 2017
We review some extensions of the continuous time random walk first introduced by Elliott Montroll and George Weiss more than 50 years ago [E.W. Montroll, G.H. Weiss, J. Math. Phys. 6, 167 (1965)], extensions that embrace multistate walks and, in particular, the persistent random walk. We generalize these extensions to include fractional random walks and derive the associated master equation, namely, the fractional telegrapher’s equation. We dedicate this review to our joint work with George H. Weiss (1930–2017). It saddens us greatly to report the recent death of George Weiss, a scientific giant and at the same time a lovely and humble man.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2017