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Tail asymptotics for the supercritical Galton-Watson process in the heavy-tailed case

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Tail asymptotics for the supercritical Galton-Watson process in the heavy-tailed case. / Wachtel, V. I.; Denisov, D. E.; Korshunov, D. A.
In: Proceedings of the Steklov Institute of Mathematics, Vol. 282, No. 1, 10.2013, p. 273-297.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Wachtel, VI, Denisov, DE & Korshunov, DA 2013, 'Tail asymptotics for the supercritical Galton-Watson process in the heavy-tailed case', Proceedings of the Steklov Institute of Mathematics, vol. 282, no. 1, pp. 273-297. https://doi.org/10.1134/S0081543813060205

APA

Wachtel, V. I., Denisov, D. E., & Korshunov, D. A. (2013). Tail asymptotics for the supercritical Galton-Watson process in the heavy-tailed case. Proceedings of the Steklov Institute of Mathematics, 282(1), 273-297. https://doi.org/10.1134/S0081543813060205

Vancouver

Wachtel VI, Denisov DE, Korshunov DA. Tail asymptotics for the supercritical Galton-Watson process in the heavy-tailed case. Proceedings of the Steklov Institute of Mathematics. 2013 Oct;282(1):273-297. Epub 2013 Oct 22. doi: 10.1134/S0081543813060205

Author

Wachtel, V. I. ; Denisov, D. E. ; Korshunov, D. A. / Tail asymptotics for the supercritical Galton-Watson process in the heavy-tailed case. In: Proceedings of the Steklov Institute of Mathematics. 2013 ; Vol. 282, No. 1. pp. 273-297.

Bibtex

@article{8d1483d7e6f14e4f8036b76e2eda469f,
title = "Tail asymptotics for the supercritical Galton-Watson process in the heavy-tailed case",
abstract = "As is well known, for a supercritical Galton-Watson process Z (n) whose offspring distribution has mean m > 1, the ratio W (n) := Z (n) /m (n) has almost surely a limit, say W. We study the tail behaviour of the distributions of W (n) and W in the case where Z (1) has a heavy-tailed distribution, that is, for every lambda > 0. We show how different types of distributions of Z (1) lead to different asymptotic behaviour of the tail of W (n) and W. We describe the most likely way in which large values of the process occur.",
keywords = "Large deviations",
author = "Wachtel, {V. I.} and Denisov, {D. E.} and Korshunov, {D. A.}",
year = "2013",
month = oct,
doi = "10.1134/S0081543813060205",
language = "English",
volume = "282",
pages = "273--297",
journal = "Proceedings of the Steklov Institute of Mathematics",
issn = "0081-5438",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "1",

}

RIS

TY - JOUR

T1 - Tail asymptotics for the supercritical Galton-Watson process in the heavy-tailed case

AU - Wachtel, V. I.

AU - Denisov, D. E.

AU - Korshunov, D. A.

PY - 2013/10

Y1 - 2013/10

N2 - As is well known, for a supercritical Galton-Watson process Z (n) whose offspring distribution has mean m > 1, the ratio W (n) := Z (n) /m (n) has almost surely a limit, say W. We study the tail behaviour of the distributions of W (n) and W in the case where Z (1) has a heavy-tailed distribution, that is, for every lambda > 0. We show how different types of distributions of Z (1) lead to different asymptotic behaviour of the tail of W (n) and W. We describe the most likely way in which large values of the process occur.

AB - As is well known, for a supercritical Galton-Watson process Z (n) whose offspring distribution has mean m > 1, the ratio W (n) := Z (n) /m (n) has almost surely a limit, say W. We study the tail behaviour of the distributions of W (n) and W in the case where Z (1) has a heavy-tailed distribution, that is, for every lambda > 0. We show how different types of distributions of Z (1) lead to different asymptotic behaviour of the tail of W (n) and W. We describe the most likely way in which large values of the process occur.

KW - Large deviations

U2 - 10.1134/S0081543813060205

DO - 10.1134/S0081543813060205

M3 - Journal article

VL - 282

SP - 273

EP - 297

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

IS - 1

ER -