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...
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| Date: | 2006 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/4440 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859508866347171840 |
|---|---|
| author | Iksanov, A. Polotskiy, S. |
| author_facet | Iksanov, A. Polotskiy, S. |
| 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. |
| collection | DSpace DC |
| 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.
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| first_indexed | 2025-11-25T15:10:05Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-4440 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0321-3900 |
| language | English |
| last_indexed | 2025-11-25T15:10:05Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Iksanov, A. Polotskiy, S. 2009-11-10T14:49:23Z 2009-11-10T14:49:23Z 2006 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 https://nasplib.isofts.kiev.ua/handle/123456789/4440 519.21 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. en Інститут математики НАН України Regular variation in the branching random walk Article published earlier |
| spellingShingle | Regular variation in the branching random walk Iksanov, A. Polotskiy, S. |
| title | 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_short | Regular variation in the branching random walk |
| title_sort | regular variation in the branching random walk |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/4440 |
| work_keys_str_mv | AT iksanova regularvariationinthebranchingrandomwalk AT polotskiys regularvariationinthebranchingrandomwalk |