Limit Theorems for Weakly Subcritical Branching Processes in Random Environment
By V. Afanasyev, Christian Boinghoff, Götz Kersting, Vladimir Vatutin. 2010
94 citations recorded by the source corpus.
For a branching process in random environment, it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the process may at the same time be subcritical and, conditioned on nonextinction, “supercritical.” This so-called weakly subcritical case is considered in this paper. We study the asymptotic survival probability and the size of the population conditioned on nonextinction. Also a functional limit theorem is proved, which makes the conditional supercriticality manifest. A main tool is a new type of functional limit theorems for conditional random walks.
Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/059a3ff650a53db622c737a7c2b94b50c9989623
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In Mathematical Physics
Citations in the corpus
- Local behaviour of first passage probabilities (2010, background): “Remark 21 The recent paper [1] contains some functional limit theorems for conditional random walks in the domain of attraction of a one-sided stable law.”