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 Cet article a éte moissonné depuis la source Journal.fi

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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 
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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/