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Random walks in cones revisited

Autor(en)
Denisov, Denis ; Wachtel, Vitali
Zeitschrift
Annales de l'Institut Henri Poincaré (B): Probability and Statistics
Normierter Zeitschriftentitel
Annales de l'Institut Henri Poincaré 
DOI
10.1214/22-AIHP1331
URL
https://pub.uni-bielefeld.de/record/2988958
Web of Science-ID
001177499400025

Weitere Details

Sprache
englisch
Darstellungsform
Text
Band
60
Ausgabe
1
Seitenbereich
126 - 166
Schlagwörter
Conditioned process , Exit time , Harmonic function , Random walk

In this paper we continue our study of a multidimensional random walk with zero mean and finite variance killed on leaving a cone. We suggest a new approach that allows one to construct a positive harmonic function in Lipschitz cones under minimal moment conditions. This approach allows also to obtain more accurate information about the behaviour of the harmonic function not far from the boundary of the cone. We also prove limit theorems under new moment conditions.

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