Infinite-dimensional diffusions as limits of random walks on partitions

Starting with finite Markov chains on partitions of a natural number n we construct, via a scaling limit transition as n → ∞, a family of infinite-dimensional diffusion processes. The limit processes are ergodic; their stationary distributions, the so-called z-measures, appeared earlier in the probl...

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Bibliographic Details
Published in:Probability theory and related fields 2009-05, Vol.144 (1-2), p.281-318
Main Authors: Borodin, Alexei, Olshanski, Grigori
Format: Article
Language:English
Subjects:
Approximation
Diffusion
Economics
Finance
Fourier analysis
Harmonic analysis
Insurance
Management
Markov analysis
Markov chains
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Probability
Probability Theory and Stochastic Processes
Quantitative Finance
Random variables
Random walk
Statistics for Business
Studies
Theoretical
Theoretical mathematics
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Description
Summary:Starting with finite Markov chains on partitions of a natural number n we construct, via a scaling limit transition as n → ∞, a family of infinite-dimensional diffusion processes. The limit processes are ergodic; their stationary distributions, the so-called z-measures, appeared earlier in the problem of harmonic analysis for the infinite symmetric group. The generators of the processes are explicitly described.
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-008-0148-8