On interweaving relations

Interweaving relations are introduced and studied here in a general Markovian setting as a strengthening of usual intertwining relations between semigroups, obtained by adding a randomized delay feature. They provide a new classification scheme of the set of Markovian semigroups which enables to tra...

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Bibliographic Details
Published in:IDEAS Working Paper Series from RePEc 2021-02, Vol.280 (3), p.108816, Article 108816
Main Authors: Miclo, Laurent, Patie, Pierre
Format: Article
Language:English
Subjects:
Economics and Finance
Entropic convergence to equilibrium
Humanities and Social Sciences
Hyperboundedness
Hypoelliptic diffusions
Interweaving relations
Laguerre processes
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Summary:Interweaving relations are introduced and studied here in a general Markovian setting as a strengthening of usual intertwining relations between semigroups, obtained by adding a randomized delay feature. They provide a new classification scheme of the set of Markovian semigroups which enables to transfer from a reference semigroup and up to an independent warm-up time, some ergodic, analytical and mixing properties including the φ-entropy convergence to equilibrium, the hyperboundedness and, when the warm-up time is deterministic, the cut-off phenomena. We also present several useful transformations that preserve interweaving relations. We provide a variety of examples of interweaving relations ranging from classical, discrete, and non-local Laguerre and Jacobi semigroups to degenerate hypoelliptic Ornstein-Uhlenbeck semigroups and some non-colliding particle systems.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2020.108816