Harmonic measure in a multidimensional gambler's problem

Autor:	Denisov, Denis, Wachtel, Vitali
Rok vydání:	2022
Předmět:	Mathematics - Probability Primary 60G50 Secondary 60F17 60G40 60J45
Druh dokumentu:	Working Paper
Popis:	We consider a random walk in a truncated cone $K_N$, which is obtained by slicing cone $K$ by a hyperplane at a growing level of order $N$. We study the behaviour of the Green function in this truncated cone as $N$ increases. Using these results we also obtain the asymptotic behaviour of the harmonic measure. The obtained results are applied to a multidimensional gambler's problem studied by Diaconis and Ethier (2022). In particular we confirm their conjecture that the probability of eliminating players in a particular order has the same exact asymptotic behaviour as for the Brownian motion approximation. We also provide a rate of convergence of this probability towards this approximation. Comment: 21 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.11526 Zobrazit plný text záznamu View this record from Arxiv