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On interweaving relations

Author

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  • Laurent Miclo

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique)

  • Pierre Patie

Abstract

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.

Suggested Citation

  • Laurent Miclo & Pierre Patie, 2021. "On interweaving relations," Post-Print hal-03159496, HAL.
    • Handle: RePEc:hal:journl:hal-03159496
    DOI: 10.1016/j.jfa.2020.108816
    Note: View the original document on HAL open archive server: https://hal.science/hal-03159496
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    References listed on IDEAS

    as
    1. Barrera, Javiera & Lachaud, Béatrice & Ycart, Bernard, 2006. "Cut-off for n-tuples of exponentially converging processes," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1433-1446, October.
    2. James Allen Fill, 2009. "On Hitting Times and Fastest Strong Stationary Times for Skip-Free and More General Chains," Journal of Theoretical Probability, Springer, vol. 22(3), pages 587-600, September.
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