A class of N-parameter Gaussian processes are introduced,which are more general than the N-parameter Wiener process.The definition of the set generated by exceptional oscillations of a class of these processes is given,and then the Hansdorff di- mension of this set is defined.The Hausdorff dimensions of these processes are studied and an exact representative for them is given,which is similar to that for the two-parameter Wiener process by Zacharie(2001).Moreover,the time set considered is a hyperrectangle which is more general than a hyper-square used by Zacharie(2001).For this more gen- eral case,a Fernique-type inequality is established and then using this inequality and the Slepian lemma,a Lévy's continuity modulus theorem is shown.Independence of incre- ments is required for showing the representative of the Hausdorff dimension by Zacharie (2001).This property is absent for the processes introduced here,so we have to find a different way.
展开▼
