A characterization of Markov processes enjoying the time-inversion property

Stephan Lawi (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We give a necessary and sufficient condition for a homogeneous Markov process taking values in $\R^n$ to enjoy the time-inversion property of degree $\alpha$. The condition sets the shape for the semigroup densities of the process and allows to further extend the class of known processes satisfying the time-inversion property. As an application we recover the result of Watanabe in \cite{Wa1975} for continuous and conservative Markov processes on $\R_+$. As new examples we generalize Dunkl processes and construct a matrix-valued process with jumps related to the Wishart process by a skew-product representation.

Mots clés: homogeneous Markov processes; time-inversion property; Bessel processes; Dunkl processes; Wishart processes; semi-stable processes

Domaines: Probabilités [math.PR]

Stephan Lawi. A characterization of Markov processes enjoying the time-inversion property. 2005. ⟨hal-00005074v2⟩