Green Function for an Asymptotically Stable Random Walk in a Half Space

Denisov D, Wachtel V (2024)
Journal of Theoretical Probability 37(2): 1745-1786.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Denisov, Denis; Wachtel, VitaliUniBi
Abstract / Bemerkung
We consider an asymptotically stable multidimensional random walk S(n) = ( S-1(n),..., S-d (n)). For every vector x = (x(1)..., x(d)) with x(1) >= 0, let tau(x) := min{n > 0 : x(1) + S-1(n) <= 0} be the first time the random walk x + S(n) leaves the upper half space. We obtain the asymptotics of p(n)(x, y) := P( x + S(n) epsilon y + Delta, tau(x) > n) as n tends to infinity, where Delta is a fixed cube. From that, we obtain the local asymptotics for the Green function G(x, y) := Sigma(n) pn(x, y), as | y| and/or |x| tend to infinity.
Stichworte
Random walk; Exit time; Harmonic function; Conditioned process
Erscheinungsjahr
2024
Zeitschriftentitel
Journal of Theoretical Probability
Band
37
Ausgabe
2
Seite(n)
1745-1786
ISSN
0894-9840
eISSN
1572-9230
Page URI
https://pub.uni-bielefeld.de/record/2984081

Zitieren

Denisov D, Wachtel V. Green Function for an Asymptotically Stable Random Walk in a Half Space. Journal of Theoretical Probability . 2024;37(2):1745-1786.
Denisov, D., & Wachtel, V. (2024). Green Function for an Asymptotically Stable Random Walk in a Half Space. Journal of Theoretical Probability , 37(2), 1745-1786. https://doi.org/10.1007/s10959-023-01283-4
Denisov, Denis, and Wachtel, Vitali. 2024. “Green Function for an Asymptotically Stable Random Walk in a Half Space”. Journal of Theoretical Probability 37 (2): 1745-1786.
Denisov, D., and Wachtel, V. (2024). Green Function for an Asymptotically Stable Random Walk in a Half Space. Journal of Theoretical Probability 37, 1745-1786.
Denisov, D., & Wachtel, V., 2024. Green Function for an Asymptotically Stable Random Walk in a Half Space. Journal of Theoretical Probability , 37(2), p 1745-1786.
D. Denisov and V. Wachtel, “Green Function for an Asymptotically Stable Random Walk in a Half Space”, Journal of Theoretical Probability , vol. 37, 2024, pp. 1745-1786.
Denisov, D., Wachtel, V.: Green Function for an Asymptotically Stable Random Walk in a Half Space. Journal of Theoretical Probability . 37, 1745-1786 (2024).
Denisov, Denis, and Wachtel, Vitali. “Green Function for an Asymptotically Stable Random Walk in a Half Space”. Journal of Theoretical Probability 37.2 (2024): 1745-1786.
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