How rich is the class of processes which are infinitely divisible with respect to time?

Khalifa Es-Sebaiy (1) , Youssef Ouknine (1)

1 UCA - Université Cadi Ayyad [Marrakech]

We give a link between stochastic processes which are infinitely divisible with respect to time (IDT) and Le´vy processes. We investigate the connection between the selfsimilarity and the strict stability for IDT processes. We also consider a subordination of a Lévy process by an increasing IDT process. We introduce a notion of multiparameter IDT stochastic processes, extending the one studied by Mansuy [2005. On processes which are infinitely divisible with respect to time. arXiv:math/0504408.]. The main example of this kind of processes is the Lévy sheet.

Mots clés: Semi-selfsimilar process; Semi-stable process; IDT process

Domaines: Probabilités [math.PR]

Khalifa Es-Sebaiy, Youssef Ouknine. How rich is the class of processes which are infinitely divisible with respect to time?. Statistics and Probability Letters, 2007, 78, pp.537-547. ⟨hal-00363616⟩