Branching Random Walk in ${\bfZ}^{4}$ with Branching at the Origin Only

For the critical branching random walk in {\bf Z}^{4} with branching at the origin we find only the asymptotic behavior of the probability of the event that there are particles at the origin at the moment t\rightarrow \infty , and we prove a Yaglom-type conditional limit theorem for the number of in...

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Bibliographic Details
Published in:Theory of probability and its applications 2012-04, Vol.56 (2), p.193-212
Main Authors: Hu, Y., Topchii, V. A., Vatutin, V. A.
Format: Article
Language:English
Subjects:
Applied mathematics
Contemporary problems
Control theory
Hypotheses
Probability
Random variables
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Summary:For the critical branching random walk in {\bf Z}^{4} with branching at the origin we find only the asymptotic behavior of the probability of the event that there are particles at the origin at the moment t\rightarrow \infty , and we prove a Yaglom-type conditional limit theorem for the number of individuals at the origin at the moment t given that there are particles at the origin.
ISSN:0040-585X
1095-7219
DOI:10.1137/S0040585X97985352