On intertwining relations between Ehrenfest, Yule and Ornstein-Uhlenbeck processes

Laurent Miclo (1, 2) , Pierre Patie (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 TSE-R - Toulouse School of Economics
3 ORIE - School of Operations Research and Information Engineering

Markovian intertwining relations between two Markov semigroups are related to the partial inclusion of the spectra of their generators, at least for finite ergodic processes. We check the limitations of this observation by investigating the Markov intertwining relations between the Ehrenfest, Yule and Ornstein-Uhlenbeck processes, whose spectra are all included into -$\mathbf{Z}_+$. As a by-product, we offer a clarification of an intertwining relation found in Biane [2] between the Yule and the Ornstein-Uhlenbeck processes.

Mots clés: Markov intertwining; Ehrenfest process; Yule process; Ornstein-Uhlenbeck process

Domaines: Probabilités [math.PR]

Laurent Miclo, Pierre Patie. On intertwining relations between Ehrenfest, Yule and Ornstein-Uhlenbeck processes. Séminaire de probabilités de Strasbourg, In press. ⟨hal-02105922⟩