Vertical and horizontal increments for the Brownian sheet, level curve's lenght and local time

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

1 UVSQ - Université de Versailles Saint-Quentin-en-Yvelines
2 UCV - Universidad Central de Venezuela

In this work we study the almost sure convergence for the vertical and horizontal increments of the Brownian sheet. Afterwards, a modification of these results for a regularization of this process, provides almost sure convergence in law for the length of the level curve, defined for the regularized process, towards a modification to the Brownian sheet's local time.

Domaines: Probabilités [math.PR]

Corinne Berzin-Joseph, José R. León. Vertical and horizontal increments for the Brownian sheet, level curve's lenght and local time. Vertical and horizontal increments for the Brownian sheet, level curve's lenght and local time, 1998, Mexico, Mexico. pp.181-191. ⟨hal-00319417⟩