Increments and crossings for the Brownian bridge: weak convergence

Corinne Berzin-Joseph (1) , José R. León (2) , Joaquín Ortega (3)

1 UVSQ - Université de Versailles Saint-Quentin-en-Yvelines
2 UCV - Universidad Central de Venezuela
3 IVIC - Departamento de Matematica

Let $b^F(t)$, $t \in [0,1]$ be an F-Brownian bridge process. We study the asymptotic behaviour of non-linear functionals of regularizations by convolution of this process and obtain several applications.

Domaines: Probabilités [math.PR]

Corinne Berzin-Joseph, José R. León, Joaquín Ortega. Increments and crossings for the Brownian bridge: weak convergence. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 1998, 327 (6), pp.587-592. ⟨10.1016/S0764-4442(98)89169-6⟩. ⟨hal-00319472⟩