Some moment results about the limit of a martingale related to the supercritical branching random walk and perpetuities
Let M(n),n=1,2,..., be the supercritical branching random walk in which the family sizes may be infinite with positive probability. Assume that a natural martingale related to M(n), converges almost surely and in the mean to a random variable W. For a large subclass of nonnegative and concave functi...
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| Datum: | 2006 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2006
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| Schriftenreihe: | Український математичний журнал |
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| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/164970 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Some moment results about the limit of a martingale related to the supercritical branching random walk and perpetuities / О.М. Iksanov // Український математичний журнал. — 2006. — Т. 58, № 4. — С. 451–471. — Бібліогр.: 23 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Let M(n),n=1,2,..., be the supercritical branching random walk in which the family sizes may be infinite with positive probability. Assume that a natural martingale related to M(n), converges almost surely and in the mean to a random variable W. For a large subclass of nonnegative and concave functions f , we provide a criterion for the finiteness of EWf(W). The main assertions of the present paper generalize some results obtained recently in Kuhlbusch’s Ph.D. thesis as well as previously known results for the Galton-Watson processes. In the process of the proof, we study the existence of the f-moments of perpetuities. |
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