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The multitype branching random walk, I
Author(s) -
Gail Ivanoff B.
Publication year - 1983
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314628
Subject(s) - random walk , statistical physics , brownian motion , limiting , branching process , branching random walk , mathematics , limit (mathematics) , supercritical fluid , stochastic process , exponential function , poisson process , poisson distribution , physics , mathematical analysis , statistics , thermodynamics , mechanical engineering , engineering
The limiting behaviour of the multitype branching random walk is studied. A limit theorem is proven for the supercritical process. Steady‐state distributions are shown to exist for the subcritical process with immigration, and for the critical transient process beginning with Poisson random fields. An analogue of the exponential limit law is proven for the critical process whose migration process is Brownian motion in two dimensions.