Almost-sure path properties of fractional Brownian sheet

doi:10.1016/j.anihpb.2006.09.005

Annales de l'Institut Henri Poincare (B) Probability and Statistics

Volume 43, Issue 5, September–October 2007, Pages 619-631

https://doi.org/10.1016/j.anihpb.2006.09.005 Get rights and content

Abstract

The almost sure sample function behavior of the vector-valued fractional Brownian sheet is investigated. In particular, the global and the local moduli of continuity of the sample functions are studied. These results give precise information about the continuity and the oscillation behavior of the sample functions.

Résumé

On étudie le comportement p.s. du mouvement brownien fractionnaire vectoriel, en particulier ses modules de continuité local et global.

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There are more references available in the full text version of this article.

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¹: The author would like to acknowledge the partial support from the Natural Science Foundation of China, grant No. 10401037.

View full text

Almost-sure path properties of fractional Brownian sheet

Abstract

Résumé

Stoch. Process. Appl.

Small ball probabilities of fractional Brownian sheets via fractional integration operators

J. Theor. Probab.

Fernique type inequalities and moduli of continuity for l2-valued Ornstein–Uhlenbeck processes

Ann. Inst. H. Poincaré Probab. Statist.

Strong Approximations in Probability and Statistics

Estimates for the small probabilities of the fractional Brownian sheet

J. Theor. Probab.

Sample function properties of multi-parameter stable processes

Z. Wahrsch. Verw. Gebiete

Fernique type inequalities and moduli of continuity for $l^{2}$ -valued Ornstein–Uhlenbeck processes