Local tail asymptotics for the joint distribution of length and of maximum of a random walk excursion
Perfilev E, Wachtel V (2022)
Theory of Probability and its Applications 67(2): 294-309.
Zeitschriftenaufsatz
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Autor*in
Perfilev, E.;
Wachtel, VitaliUniBi
Einrichtung
Abstract / Bemerkung
This note is devoted to the study of the maximum of the excursion of a random walk with negative drift and light-tailed increments. More precisely, we determine the local asymptotics of the joint distribution of the length, the maximum, and the time at which this maximum is achieved. This result allows one to obtain a local central limit theorem for the length of the excursion conditioned on large values of the maximum.
Stichworte
random walk;
excursion;
Crame?r-Lundberg;
exponential change of measure
Erscheinungsjahr
2022
Zeitschriftentitel
Theory of Probability and its Applications
Band
67
Ausgabe
2
Seite(n)
294-309
ISSN
0040-585X
eISSN
1095-7219
Page URI
https://pub.uni-bielefeld.de/record/2968208
Zitieren
Perfilev E, Wachtel V. Local tail asymptotics for the joint distribution of length and of maximum of a random walk excursion. Theory of Probability and its Applications. 2022;67(2):294-309.
Perfilev, E., & Wachtel, V. (2022). Local tail asymptotics for the joint distribution of length and of maximum of a random walk excursion. Theory of Probability and its Applications, 67(2), 294-309. https://doi.org/10.1137/S0040585X97T990939
Perfilev, E., and Wachtel, Vitali. 2022. “Local tail asymptotics for the joint distribution of length and of maximum of a random walk excursion”. Theory of Probability and its Applications 67 (2): 294-309.
Perfilev, E., and Wachtel, V. (2022). Local tail asymptotics for the joint distribution of length and of maximum of a random walk excursion. Theory of Probability and its Applications 67, 294-309.
Perfilev, E., & Wachtel, V., 2022. Local tail asymptotics for the joint distribution of length and of maximum of a random walk excursion. Theory of Probability and its Applications, 67(2), p 294-309.
E. Perfilev and V. Wachtel, “Local tail asymptotics for the joint distribution of length and of maximum of a random walk excursion”, Theory of Probability and its Applications, vol. 67, 2022, pp. 294-309.
Perfilev, E., Wachtel, V.: Local tail asymptotics for the joint distribution of length and of maximum of a random walk excursion. Theory of Probability and its Applications. 67, 294-309 (2022).
Perfilev, E., and Wachtel, Vitali. “Local tail asymptotics for the joint distribution of length and of maximum of a random walk excursion”. Theory of Probability and its Applications 67.2 (2022): 294-309.
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