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Critical behavior of some measure‐valued processes
Author(s) -
Fleischmann Klaus
Publication year - 1988
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19881350114
Subject(s) - mathematics , measure (data warehouse) , dimension (graph theory) , branching process , critical dimension , space (punctuation) , absolute continuity , field (mathematics) , branching (polymer chemistry) , pure mathematics , statistical physics , combinatorics , physics , quantum mechanics , linguistics , philosophy , database , computer science , materials science , composite material
The so‐called weighted occupation time process Y associated with some critical measur‐evalued branching process is considered. Y has absolutely continuous states provided that the dimension of the phase space is small enough. The corresponding density functions form a random process η. In some cases there exists a critical dimension such that η. considered in the space‐time diagram, is a self‐similar random non‐negative field. This self‐similar field is infinitely divisible but not stable.