Geodesic
On the finiteness of moments of the exit time of planar Brownian motion from comb domains
Maher Boudabra1 ; Greg Markowsky1
1 Monash University, Department of Mathematics
Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 527-536.

Voir la notice de l'article provenant de la source Journal.fi

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 $p \geq 1/2$.
Keywords: Planar Brownian motion, exit time

Maher Boudabra 1 ; Greg Markowsky 1

1 Monash University, Department of Mathematics 
@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},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2021},
     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
PB  - mathdoc
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
%I mathdoc
%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/