L_1-distance for additive processes with time-homogeneous Lévy measures

Pierre Etoré (1) , Ester Mariucci (1)

1 IPS - Inférence Processus Stochastiques

We give an explicit bound for the $L_1$-distance between two additive processes of local characteristics $(f_j(\cdot),\sigma^2(\cdot),\nu_j)$, $j = 1,2$. The cases $\sigma =0$ and $\sigma > 0$ are both treated. We allow $\nu_1$ and $\nu_2$ to be equivalent time-homogeneous Lévy measures, possibly with infinite variation. Some examples of possible applications are discussed.

Mots clés: Lévy Processes; Additive Processes; $L_1$-distance

Domaines: Probabilités [math.PR]

Pierre Etoré, Ester Mariucci. L_1-distance for additive processes with time-homogeneous Lévy measures. Electronic Communications in Probability, 2014, 19 (paper no. 57), 10 pp. ⟨10.1214/ECP.v19-3678⟩. ⟨hal-00985588v2⟩