Regular variation in the branching random walk

initial ancestor located at the origin of the real line. For n = 0, 1, . . . , let Wn be the moment generating function of Mn normalized by its mean. Denote by AWn any of the following random variables: maximal function, square function, L1 and a.s. limit W, supn≥0 |W − Wn|, supn≥0 |Wn+1 − Wn|. Un...

Повний опис

Збережено в:

Бібліографічні деталі
Видавець:	Інститут математики НАН України
Дата:	2006
Автори:	Iksanov, A., Polotskiy, S.
Формат:	Стаття
Мова:	English
Опубліковано:	Інститут математики НАН України 2006
Онлайн доступ:	http://dspace.nbuv.gov.ua/handle/123456789/4440
Теги:	Додати тег Немає тегів, Будьте першим, хто поставить тег для цього запису!
Цитувати:	Regular variation in the branching random walk / A. Iksanov, S. Polotskiy // Theory of Stochastic Processes. — 2006. — Т. 12 (28), № 1-2. — С. 38–54. — Бібліогр.: 25 назв.— англ.

Репозиторії

Digital Library of Periodicals of National Academy of Sciences of Ukraine

id	irk-123456789-4440
record_format	dspace
spelling	irk-123456789-44402009-11-11T12:00:33Z Regular variation in the branching random walk Iksanov, A. Polotskiy, S. initial ancestor located at the origin of the real line. For n = 0, 1, . . . , let Wn be the moment generating function of Mn normalized by its mean. Denote by AWn any of the following random variables: maximal function, square function, L1 and a.s. limit W, supn≥0 \|W − Wn\|, supn≥0 \|Wn+1 − Wn\|. Under mild moment restrictions and the assumption that {W1 > x} regularly varies at ∞, it is proved that P{AWn > x} regularly varies at ∞ with the same exponent. All the proofs given are non-analytic in the sense that these do not use Laplace–Stieltjes transforms. The result on the tail behaviour of W is established in two distinct ways. 2006 Article Regular variation in the branching random walk / A. Iksanov, S. Polotskiy // Theory of Stochastic Processes. — 2006. — Т. 12 (28), № 1-2. — С. 38–54. — Бібліогр.: 25 назв.— англ. 0321-3900 http://dspace.nbuv.gov.ua/handle/123456789/4440 519.21 en Інститут математики НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
description	initial ancestor located at the origin of the real line. For n = 0, 1, . . . , let Wn be the moment generating function of Mn normalized by its mean. Denote by AWn any of the following random variables: maximal function, square function, L1 and a.s. limit W, supn≥0 \|W − Wn\|, supn≥0 \|Wn+1 − Wn\|. Under mild moment restrictions and the assumption that {W1 > x} regularly varies at ∞, it is proved that P{AWn > x} regularly varies at ∞ with the same exponent. All the proofs given are non-analytic in the sense that these do not use Laplace–Stieltjes transforms. The result on the tail behaviour of W is established in two distinct ways.
format	Article
author	Iksanov, A. Polotskiy, S.
spellingShingle	Iksanov, A. Polotskiy, S. Regular variation in the branching random walk
author_facet	Iksanov, A. Polotskiy, S.
author_sort	Iksanov, A.
title	Regular variation in the branching random walk
title_short	Regular variation in the branching random walk
title_full	Regular variation in the branching random walk
title_fullStr	Regular variation in the branching random walk
title_full_unstemmed	Regular variation in the branching random walk
title_sort	regular variation in the branching random walk
publisher	Інститут математики НАН України
publishDate	2006
url	http://dspace.nbuv.gov.ua/handle/123456789/4440
citation_txt	Regular variation in the branching random walk / A. Iksanov, S. Polotskiy // Theory of Stochastic Processes. — 2006. — Т. 12 (28), № 1-2. — С. 38–54. — Бібліогр.: 25 назв.— англ.
work_keys_str_mv	AT iksanova regularvariationinthebranchingrandomwalk AT polotskiys regularvariationinthebranchingrandomwalk
first_indexed	2023-03-24T08:30:10Z
last_indexed	2023-03-24T08:30:10Z
_version_	1796139180827344896

Regular variation in the branching random walk

Репозиторії

Схожі ресурси