Greven A (1991)
Publication Language: English
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 1991
Publisher: Springer Verlag (Germany)
Book Volume: 87
Pages Range: 417-458
Journal Issue: 4
DOI: 10.1007/BF01304274
We consider a particular Markov process η on ℕ, S=ℤ. The random variable η(x) is interpreted as the number of particles at x at time t. The initial distribution of this process is a translation invariant measure μ with fη(x)dμ<∞. The evolution is as follows: At rate bη(x) a particle is born at x but moves instantaneously to y chosen with probability q(x, y). All particles at a site die at rate pd with p∈[0, 1], d,∈ ℝ and individual particles die independently from each other at rate (1-p)d. Every particle moves independently of everything else according to a continuous time random walk. We are mainly interested in the case b=d and n≧3. The process exhibits a phase transition with respect to the parameter p: For p
p,) converges as t→∞ to the measure concentrated on the configuration identically 0. We calculate p as well as p, the points with the property that the extremal invariant measures have for p>p infinite n-th moment of η(x) and for p
p>p>p≧...≧p>0, p↓0 occurs for suitable values of the other parameters. For p
APA:
Greven, A. (1991). A phase transition for the coupled branching process - Part I: The ergodic theory in the range of finite second moments. Probability Theory and Related Fields, 87(4), 417-458. https://dx.doi.org/10.1007/BF01304274
MLA:
Greven, Andreas. "A phase transition for the coupled branching process - Part I: The ergodic theory in the range of finite second moments." Probability Theory and Related Fields 87.4 (1991): 417-458.
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