scholarly journals Diffusion coefficients for multi-step persistent random walks on lattices

2009 ◽  
Vol 43 (3) ◽  
pp. 035001 ◽  
Author(s):  
Thomas Gilbert ◽  
David P Sanders
Keyword(s):  
Random Walks ◽  
Diffusion Coefficients ◽  
Persistent Random Walks

scholarly journals Non-homogeneous persistent random walks and Lévy–Lorentz gas

2018 ◽  
Vol 2018 (8) ◽  
pp. 083209 ◽  
Author(s):  
Roberto Artuso ◽  
Giampaolo Cristadoro ◽  
Manuele Onofri ◽  
Mattia Radice
Keyword(s):  
Random Walks ◽  
Lorentz Gas ◽  
Persistent Random Walks

scholarly journals FROM PERSISTENT RANDOM WALK TO THE TELEGRAPH NOISE

2010 ◽  
Vol 10 (02) ◽  
pp. 161-196 ◽  
Author(s):  
S. HERRMANN ◽  
P. VALLOIS
Keyword(s):  
Random Walk ◽  
Markov Process ◽  
Random Walks ◽  
Poisson Process ◽  
Counting Process ◽  
Telegraph Equation ◽  
Space Time ◽  
Persistent Random Walks ◽  
Persistent Random Walk ◽  
Telegraph Noise

We study a family of memory-based persistent random walks and we prove weak convergences after space-time rescaling. The limit processes are not only Brownian motions with drift. We have obtained a continuous but non-Markov process (Zt) which can be easily expressed in terms of a counting process (Nt). In a particular case the counting process is a Poisson process, and (Zt) permits to represent the solution of the telegraph equation. We study in detail the Markov process ((Zt, Nt); t ≥ 0).

scholarly journals Reaction fronts in persistent random walks with demographic stochasticity

2019 ◽  
Vol 99 (1) ◽  
Author(s):  
Davide Vergni ◽  
Stefano Berti ◽  
Angelo Vulpiani ◽  
Massimo Cencini
Keyword(s):  
Random Walks ◽  
Demographic Stochasticity ◽  
Reaction Fronts ◽  
Persistent Random Walks

scholarly journals Recurrence of multidimensional persistent random walks. Fourier and series criteria

Bernoulli ◽  
2020 ◽  
Vol 26 (2) ◽  
pp. 858-892
Author(s):  
Peggy Cénac ◽  
Basile de Loynes ◽  
Yoann Offret ◽  
Arnaud Rousselle
Keyword(s):  
Random Walks ◽  
Persistent Random Walks ◽  
Series Criteria

Search along persistent random walks

2008 ◽  
Vol 5 (2) ◽  
pp. 026007 ◽  
Author(s):  
Benjamin M Friedrich
Keyword(s):  
Random Walks ◽  
Persistent Random Walks

scholarly journals RECURRENCE FOR PERSISTENT RANDOM WALKS IN TWO DIMENSIONS

2007 ◽  
Vol 07 (01) ◽  
pp. 53-74 ◽  
Author(s):  
MARCO LENCI
Keyword(s):  
Random Walks ◽  
Large Class ◽  
Transition Probabilities ◽  
Two Dimensions ◽  
Random Environments ◽  
Geometric Features ◽  
Persistent Random Walks

We discuss the question of recurrence for persistent, or Newtonian, random walks in ℤ2, i.e. random walks whose transition probabilities depend both on the walker's position and incoming direction. We use results by Tóth and Schmidt–Conze to prove recurrence for a large class of such processes, including all "invertible" walks in elliptic random environments. Furthermore, rewriting our Newtonian walks as ordinary random walks in a suitable graph, we gain a better idea of the geometric features of the problem, and obtain further examples of recurrence.

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