In this paper, we are interested in the asymptotic behaviour of the sequence of processes (W$$(s,t))$$ with
| $$ |
where (ξ$$, x ∈ ℤ$$) is a sequence of independent random variables uniformly distributed on [0, 1] and (S$$)$$ is a random walk evolving in ℤ$$, independent of the ξ’s. In M. Wendler [Stoch. Process. Appl. 126 (2016) 2787–2799], the case where (S$$)$$ is a recurrent random walk in ℤ such that (n$$S$$)$$ converges in distribution to a stable distribution of index α, with α ∈ (1, 2], has been investigated. Here, we consider the cases where (S$$)$$ is either:
(a) a transient random walk in ℤ$$,
(b) a recurrent random walk in ℤ$$ such that (n$$S$$)$$ converges in distribution to a stable distribution of index d ∈{1, 2}.
Accepté le :
Première publication :
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DOI : 10.1051/ps/2019030
Mots-clés : Random walk, random scenery, empirical process
@article{PS_2020__24_1_127_0,
author = {Guillotin-Plantard, Nadine and P\`ene, Fran\c{c}oise and Wendler, Martin},
title = {Empirical processes for recurrent and transient random walks in random scenery},
journal = {ESAIM: Probability and Statistics},
pages = {127--137},
publisher = {EDP-Sciences},
volume = {24},
year = {2020},
doi = {10.1051/ps/2019030},
mrnumber = {4071316},
zbl = {1447.60073},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2019030/}
}
TY - JOUR AU - Guillotin-Plantard, Nadine AU - Pène, Françoise AU - Wendler, Martin TI - Empirical processes for recurrent and transient random walks in random scenery JO - ESAIM: Probability and Statistics PY - 2020 SP - 127 EP - 137 VL - 24 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2019030/ DO - 10.1051/ps/2019030 LA - en ID - PS_2020__24_1_127_0 ER -
%0 Journal Article %A Guillotin-Plantard, Nadine %A Pène, Françoise %A Wendler, Martin %T Empirical processes for recurrent and transient random walks in random scenery %J ESAIM: Probability and Statistics %D 2020 %P 127-137 %V 24 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2019030/ %R 10.1051/ps/2019030 %G en %F PS_2020__24_1_127_0
Guillotin-Plantard, Nadine; Pène, Françoise; Wendler, Martin. Empirical processes for recurrent and transient random walks in random scenery. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 127-137. doi : 10.1051/ps/2019030. http://archive.numdam.org/articles/10.1051/ps/2019030/
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