Sharpness of second moment criteria for branching and tree-indexed processes
نویسنده
چکیده
A class of branching processes in varying environments is exhibited which become extinct almost surely even though the means Mn grow fast enough so that ∑ M−1 n is finite. In fact, such a process is constructed for every offspring distribution of infinite variance, and this establishes the converse of a previously known fact: that if a distribution has finite variance then ∑ M−1 n = ∞ is equivalent to almost sure extinction. This has as an immediate consequence the converse to a theorem on equipolarity of Galton-Watson trees.
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تاریخ انتشار 2003