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- W2105497908 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 $left(h,lambdaright)$, where $h$ is an $R$-harmonic function on $X$, and $lambda$ 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 $mathbb{P}$ 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 $mathbb{P}$ quasi-invariant with respect to a shift automorphism. The latter takes the form of explicit multi-resolutions in $L^{2}$ of $mathbb{P}$ in the sense of Lax-Phillips scattering theory." @default.
- W2105497908 created "2016-06-24" @default.
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- W2105497908 date "2015-10-19" @default.
- W2105497908 modified "2023-09-26" @default.
- W2105497908 title "Transfer Operators, Induced Probability Spaces, and Random Walk Models" @default.
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- W2105497908 doi "https://doi.org/10.48550/arxiv.1510.05573" @default.
- W2105497908 hasPublicationYear "2015" @default.
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