Abstract.
The main result in this paper states that if a one-parameter Gaussian process has C 2k paths and satisfies a non-degeneracy condition, then the distribution of its maximum on a compact interval is of class C k. The methods leading to this theorem permit also to give bounds on the successive derivatives of the distribution of the maximum and to study their asymptotic behaviour as the level tends to infinity.
Article PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 14 May 1999 / Revised version: 18 October 1999 / Published online: 14 December 2000
Rights and permissions
About this article
Cite this article
Azaïs, JM., Wschebor, M. On the regularity of the distribution of the maximum of one-parameter Gaussian processes. Probab Theory Relat Fields 119, 70–98 (2001). https://doi.org/10.1007/PL00012739
Issue Date:
DOI: https://doi.org/10.1007/PL00012739