Beta-gamma random variables and intertwining relations between certain Markov processes

Reflected planar Brownian motions, intertwining relations and crossing probabilities

“…One may remark that these intertwining relations fit in the "filtering type framework" described in [CPY98].…”

“…First, let us recall the notion of intertwined Markovian semigroups (for some background on the subject, see [CPY98]). Let (P t , t ≥ 0) and (Q t , t ≥ 0) be two Markovian semigroups with respective state spaces (S P , S P ) and (S Q , S Q ), and Λ a Markov transition kernel from (S Q , S Q ) to (S P , S P ).…”

“…More precisely, the projection of the RBM on the symmetry axis is a diffusion in its own filtration; for wedges, one recovers the 3-dimensional Bessel process. This provides a new example of non-trivial intertwining relations (see for instance [RogPit81,CPY98]). Our proofs rely also on reflected simple random walks and an invariance principle.…”

Hitting Times and Interlacing Eigenvalues: A Stochastic Approach Using Intertwinings

“…The main conceptual tool in our approach is the notion of an intertwining of Markov semigroups, for which we now provide the needed background in the context (sufficient for our purposes) of finitestate Markov chains. For further background on intertwinings, see [4], [8], [26]. Suppose that we have two state spaces, the first ("primary") of size n and the second ("dual") of sizen.…”

Entrelacements de semi-groupes provenant de paires de Gelfand

“…La notion d'entrelacement de noyaux markoviens, ou de semi-groupes de tels noyaux, a fait l'objet de plusieurs travaux de Carmona et al [6] (dont Yor), et Hirsch et Yor [13]. Elle s'est révélée très utile dans plusieurs problèmes concernant les processus stochastiques, on pourra voir par exemple [9], [14] et [15] pour plusieurs développements récents.…”