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The Fractal Character of Localizable Measure‐Valued Processes, III. Fractal Carrying Sets of Branching Diffusions
Author(s) -
Zähle U.
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.19881380121
Subject(s) - mathematics , branching (polymer chemistry) , fractal , infinitesimal , fractal dimension , statistical physics , population , measure (data warehouse) , character (mathematics) , pure mathematics , mathematical analysis , geometry , physics , computer science , materials science , demography , database , sociology , composite material
Regard a large population of infinitesimal particles (i.e. measures) in the case, when the particles evolve (i.e. move, branch, die) independently of each other. Those evolutions we called localizable. In the present part of this paper we study branching diffusion processes, which result from high frequent alternations of pure macroscopic motion and a pure branching mechanism. The main aim is to compute the H AUSDORFF ‐B ESICOVITCH dimension of random sets carrying the population.