A comb domain is defined to be the entire complex plain with a collection of vertical slits, symmetric over the real axis, removed. In this paper, we consider the question of determining whether the exit time of planar Brownian motion from such a domain has finite $p$-th moment. This question has been addressed before in relation to starlike domains, but these previous results do not apply to comb domains. Our main result is a sufficient condition on the location of the slits which ensures that the $p$-th moment of the exit time is finite. Several auxiliary results are also presented, including a construction of a comb domain whose exit time has infinite $p$-th moment for all $p \geq 1/2$.
@article{AFM_2021_46_1_a30,
author = {Maher Boudabra and Greg Markowsky},
title = {On the finiteness of moments of the exit time of planar {Brownian} motion from comb domains},
journal = {Annales Fennici Mathematici},
pages = {527--536},
year = {2021},
volume = {46},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a30/}
}
TY - JOUR
AU - Maher Boudabra
AU - Greg Markowsky
TI - On the finiteness of moments of the exit time of planar Brownian motion from comb domains
JO - Annales Fennici Mathematici
PY - 2021
SP - 527
EP - 536
VL - 46
IS - 1
UR - http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a30/
LA - en
ID - AFM_2021_46_1_a30
ER -
%0 Journal Article
%A Maher Boudabra
%A Greg Markowsky
%T On the finiteness of moments of the exit time of planar Brownian motion from comb domains
%J Annales Fennici Mathematici
%D 2021
%P 527-536
%V 46
%N 1
%U http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a30/
%G en
%F AFM_2021_46_1_a30
Maher Boudabra; Greg Markowsky. On the finiteness of moments of the exit time of planar Brownian motion from comb domains. Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 527-536. http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a30/
