Beta-gamma random variables and intertwining relations between certain Markov processes (Q1271363)

The paper deals with the intertwining relation of two semigroups \((P_t)\) and \((Q_t)\) of Markov processes on possibly different state spaces with respect to a Markov kernel \(\Lambda\) from one space to the other: \(Q_t \Lambda = \Lambda P_t\). Six concrete examples are presented to illustrate the relation. Some detail properties of the resulting processes are studied. The relationship of the above notion with the duality with respect to a probability measure or a function is also established. It seems to the reviewer that such a relation should have a wider range of applications.