2021/01/18 by Maher Boudabra, Boudabra, Maher, Greg Markowsky +1 · 1 citation
Mathematics · #Analytic and geometric function theory #Holomorphic and Operator Theory #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2101.06895
A comb domain is defined to be the entire complex plain with a collection of\nvertical slits, symmetric over the real axis, removed. In this paper, we\nconsider the question of determining whether the exit time of planar Brownian\nmotion from such a domain has finite p-th moment. This question has been\naddressed before in relation to starlike domains, but these previous results do\nnot apply to comb domains. Our main result is a sufficient condition on the\nlocation of the slits which ensures that the p-th moment of the exit time is\nfinite. Several auxiliary results are also presented, including a construction\nof a comb domain whose exit time has infinite p-th moment for all p \≥\n1/2.\n