Journal article
Transfer Operators, Induced Probability Spaces, and Random Walk Models
Markov processes and related fields, Vol.23(2), pp.187-210
01/01/2017
Abstract
We study a family of discrete-time random-walk models. The starting point is a fixed generalized transfer operator R subject to a set of axioms, and a given endomorphism in a compact Hausdorff space X. Our setup includes a host of models from applied dynamical systems, and it leads to general path space probability realizations of the initial transfer operator. The analytic data in our construction is a pair (h, lambda), where h is an R-harmonic function on X, and A is a given positive measure on X subject to a certain invariance condition defined from R. With this we show that there are then discrete-time random walk realizations in explicit path-space models; each associated to a probability measures P on path-space, in such a way that the initial data allows for spectral characterization: The initial endomorphism in X lifts to an automorphism in path-space with the probability measure P quasi-invariant with respect to a shift automorphism. The latter takes the form of explicit multiresolutions in L-2 of P in the sense of Lax-Phillips scattering theory.
Details
- Title: Subtitle
- Transfer Operators, Induced Probability Spaces, and Random Walk Models
- Creators
- P Jorgensen - Univ Iowa, Dept Math, Iowa City, IA 52242 USAF Tian - Hampton University
- Resource Type
- Journal article
- Publication Details
- Markov processes and related fields, Vol.23(2), pp.187-210
- Publisher
- POLYMAT
- ISSN
- 1024-2953
- Number of pages
- 24
- Language
- English
- Date published
- 01/01/2017
- Academic Unit
- Mathematics
- Record Identifier
- 9984242430702771
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