A concentration inequality for inhomogeneous Neymann-Scott point processes

Jean-François Coeurjolly (1) , Patricia Reynaud-Bouret (2)

1 UQAM - Université du Québec à Montréal = University of Québec in Montréal
2 LJAD - Laboratoire Jean Alexandre Dieudonné

In this note, we prove some non-asymptotic concentration inequalities for functionals, called innovations, of inhomogeneous Neymann-Scott point processes, a particular class of spatial point process models. Innovation is a functional built from the counting measure minus its integral compensator. The result is then applied to obtain almost sure rate of convergence for such functionals.

Mots clés: Spatial point processes; Almost sure convergence rate; Deviation inequalities; Campbell's Theorem

Domaines: Statistiques [math.ST]; Probabilités [math.PR]; Théorie [stat.TH]

Jean-François Coeurjolly, Patricia Reynaud-Bouret. A concentration inequality for inhomogeneous Neymann-Scott point processes. Statistics and Probability Letters, 2019, 148. ⟨hal-02456693⟩