Inversion, duality and Doob $h$-transforms for self-similar Markov processes

Larbi Alili, Loïc Chaumont, Piotr Graczyk +1

We show that any ${\mathbb{R}}^d\setminus \{0\}$-valued self-similar Markov process $X$, with index $\alpha >0$ can be represented as a path transformation of some Markov additive process (…