Regular variation in the branching random walk
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Regular variation in the branching random walk
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| Creator |
Iksanov, A.
Polotskiy, S. |
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| 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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| Date |
2009-11-10T14:49:23Z
2009-11-10T14:49:23Z 2006 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Publisher |
Інститут математики НАН України
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