Occupation Density and Sample Path Properties

Abstract

0 Introduction 0.1 Gaussian (N, d)-fields 0.2 (\(N,d, \alpha\))-stable Lévy sheets 0.3 Other fields 1 Occupation density of a function and the Hausdorff dimension of its level sets 1.1 Occupation density of a function 1.2 Hölder continuity and Hausdorff dimension 1.A Fourier transform of multivariate measures 2 Occupation density of Gaussian (N, d)-fields 2.1 Covariance and occupation density 2.2 Joint continuity and Hölder conditions 2.3 (N,d)- fractional Brownian motion and Brownian sheet 3 Occupation density of (\(N,d, \alpha\))-stable Lévy sheets 3.1 Definitions 3.2 Joint continuity and Hölder conditions 3.3 Asymptotic behaviour of occupation integrals References