Geometric aspects of Fleming-Viot and Dawson-Watanabe processes
نویسندگان
چکیده
منابع مشابه
Geometric aspects of Fleming-Viot and superprocesses
The main purpose of this paper is to show that the intrinsic metric of the Fleming-Viot process is given by anàngular distance' on the space of probability measures. It turns out that it is closely related to the branching structure of a continuous superprocess, which itself induces the Kakutani-Hellinger distance. The corresponding ge-ometries are studied in some detail. In particular, represe...
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In 1991 Perkins [7] showed that the normalized critical binary branching process is a time inhomogeneous Fleming-Viot process. In the present paper we extend this result to jump-type branching processes and we show that the normalized jump-type branching processes are in a new class of probability measure-valued processes which will be called “jump-type Fleming-Viot processes”. Furthermore we a...
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Fleming-Viot process is a mathematical model in population genetics. It is a probabilitymeasure-valued process describing the relative frequencies of allelic types in a large population undergoing mutation, selection and genetic drift. The interacting Fleming-Viot process describes the evolution of a collection of Fleming-Viot processes in which those Fleming-Viot processes interact with each o...
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We consider an irreducible pure jump Markov process with rates Q = (q(x, y)) on Λ ∪ {0} with Λ countable and 0 an absorbing state. A quasi stationary distribution (qsd) is a probability measure ν on Λ that satisfies: starting with ν, the conditional distribution at time t, given that at time t the process has not been absorbed, is still ν. That is, ν(x) = νPt(x)/( ∑ y∈Λ νPt(y)), with Pt the tra...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1997
ISSN: 0091-1798
DOI: 10.1214/aop/1024404509