1. Normalization of a critical branching process in a random environment
- Author
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Guivarc'h, Yves, Le Page, Emile, and Liu, Quansheng
- Subjects
- *
STOCHASTIC processes , *PROBABILITY theory , *GENERATING functions , *COMBINATORICS , *MATHEMATICS - Abstract
Let
(Zn) be a critical branching process in an independent and identically distributed (i.i.d.) random environment. For each fixed environmentω , letCn=Eω[Zn∣Zn>0] be the conditional expectation ofZn givenZn>0 . We prove an analogue of Yaglom''s law: asn→∞ , the conditional law ofZn/Cn , conditional onZn>0 , converges to a non-degenerate law on[0,∞) . We give also an analogue of Kolmogorov''s law, as well as a local limit theorem for the semi-group of probability generating functions. To cite this article: Y. Guivarc''h et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003). [Copyright &y& Elsevier]- Published
- 2003
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