1Hugo Steinhaus Center Institute of Mathematics and Computer Science Wrocław University of Technology 50-370 Wrocław, Poland 2Department of Statistics and Probability Michigan State University East Lansing, MI 48824, U.S.A. 3Fachbereich Mathematik Universität Siegen 57068 Siegen, Germany
Studia Mathematica, Tome 205 (2011) no. 1, pp. 13-30
In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW model is useful in physics, to model diffusing particles. Its scaling limit is a time-changed process, whose densities solve an anomalous diffusion equation. This paper develops limit theory and governing equations for cluster CTRW, in which a random number of jumps cluster together into a single jump. The clustering introduces a dependence between the waiting times and jumps that significantly affects the asymptotic limit. Vector jumps are considered, along with oracle CTRW, where the process anticipates the next jump.
Keywords:
continuous time random walk ctrw random waiting time precedes each random jump ctrw model useful physics model diffusing particles its scaling limit time changed process whose densities solve anomalous diffusion equation paper develops limit theory governing equations cluster ctrw which random number jumps cluster together single jump clustering introduces dependence between waiting times jumps significantly affects asymptotic limit vector jumps considered along oracle ctrw where process anticipates jump
Affiliations des auteurs :
Agnieszka Jurlewicz
1
;
Mark M. Meerschaert
2
;
Hans-Peter Scheffler
3
1
Hugo Steinhaus Center Institute of Mathematics and Computer Science Wrocław University of Technology 50-370 Wrocław, Poland
2
Department of Statistics and Probability Michigan State University East Lansing, MI 48824, U.S.A.
3
Fachbereich Mathematik Universität Siegen 57068 Siegen, Germany
@article{10_4064_sm205_1_2,
author = {Agnieszka Jurlewicz and Mark M. Meerschaert and Hans-Peter Scheffler},
title = {Cluster continuous time random walks},
journal = {Studia Mathematica},
pages = {13--30},
year = {2011},
volume = {205},
number = {1},
doi = {10.4064/sm205-1-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm205-1-2/}
}
TY - JOUR
AU - Agnieszka Jurlewicz
AU - Mark M. Meerschaert
AU - Hans-Peter Scheffler
TI - Cluster continuous time random walks
JO - Studia Mathematica
PY - 2011
SP - 13
EP - 30
VL - 205
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4064/sm205-1-2/
DO - 10.4064/sm205-1-2
LA - en
ID - 10_4064_sm205_1_2
ER -
%0 Journal Article
%A Agnieszka Jurlewicz
%A Mark M. Meerschaert
%A Hans-Peter Scheffler
%T Cluster continuous time random walks
%J Studia Mathematica
%D 2011
%P 13-30
%V 205
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/sm205-1-2/
%R 10.4064/sm205-1-2
%G en
%F 10_4064_sm205_1_2
Agnieszka Jurlewicz; Mark M. Meerschaert; Hans-Peter Scheffler. Cluster continuous time random walks. Studia Mathematica, Tome 205 (2011) no. 1, pp. 13-30. doi: 10.4064/sm205-1-2
