Harmonic measure in a multidimensional gambler’s problem
Denisov D, Wachtel V (2024)
Annals of Applied Probability 34(5): 4387-4407.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Autor*in
Denisov, Denis;
Wachtel, VitaliUniBi
Einrichtung
Abstract / Bemerkung
We consider a random walk in a truncated cone KN, 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 The obtained results are applied to a multidimensional gambler's problem studied by Diaconis and Ethier (Staist. Sci. 37 (2022) 289-305). 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.
Stichworte
Random walk;
Brownian motion;
first-passage time;
overshoot;
moving;
boundary
Erscheinungsjahr
2024
Zeitschriftentitel
Annals of Applied Probability
Band
34
Ausgabe
5
Seite(n)
4387-4407
ISSN
1050-5164
Page URI
https://pub.uni-bielefeld.de/record/2999514
Zitieren
Denisov D, Wachtel V. Harmonic measure in a multidimensional gambler’s problem. Annals of Applied Probability. 2024;34(5):4387-4407.
Denisov, D., & Wachtel, V. (2024). Harmonic measure in a multidimensional gambler’s problem. Annals of Applied Probability, 34(5), 4387-4407. https://doi.org/10.1214/24-AAP2069
Denisov, Denis, and Wachtel, Vitali. 2024. “Harmonic measure in a multidimensional gambler’s problem”. Annals of Applied Probability 34 (5): 4387-4407.
Denisov, D., and Wachtel, V. (2024). Harmonic measure in a multidimensional gambler’s problem. Annals of Applied Probability 34, 4387-4407.
Denisov, D., & Wachtel, V., 2024. Harmonic measure in a multidimensional gambler’s problem. Annals of Applied Probability, 34(5), p 4387-4407.
D. Denisov and V. Wachtel, “Harmonic measure in a multidimensional gambler’s problem”, Annals of Applied Probability, vol. 34, 2024, pp. 4387-4407.
Denisov, D., Wachtel, V.: Harmonic measure in a multidimensional gambler’s problem. Annals of Applied Probability. 34, 4387-4407 (2024).
Denisov, Denis, and Wachtel, Vitali. “Harmonic measure in a multidimensional gambler’s problem”. Annals of Applied Probability 34.5 (2024): 4387-4407.
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