Almost sure behavior of functionals of stationary Gibbs point processes

Jean-François Coeurjolly (1)

1 FIGAL - Fiabilité et Géométrie Aléatoire

This paper is concerned with the almost sure control of functionals of stationary Gibbs point processes. We apply Kahane–Khintchine’s inequality to derive an almost sure control of various functionals under very mild assumption on the spatial point process X. In particular, if X is a locally stable Gibbs point process with finite range observed in [−n,n]^d, we obtain the bound N_[−n,n]d(X)/(2n)d=ρ+O_a.s.(n^−d/2log n^3/2) as n→∞, where N_W(X) is the number of points of X∩W for W⊂R^d and where ρ is the intensity parameter of X.

Mots clés: Kahane–Khintchine’s inequality; Luxemburg norm; Gibbs point process; Georgii–Nguyen–Zessin formula

Domaines: Statistiques [math.ST]

Jean-François Coeurjolly. Almost sure behavior of functionals of stationary Gibbs point processes. Statistics and Probability Letters, 2015, 97, pp.241-246. ⟨10.1016/j.spl.2014.11.014⟩. ⟨hal-01154829⟩