In this paper,we obtain functional limit theorems for d-dimensional FBM in Hlder normvia estimating large deviation probabilities for d-dimensional FBM
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.
We introduce a super-Lévy process and study maximal speed of all particles in the range and the support of the super-Lévy process.The state of historical super-Lévy process is a measure on the set of paths.We study the maximal speed of all particles during a given time period,which turns out to be a function of the packing dimension of the time period.We calculate the Hausdorff dimension of the set of a-fast paths in the support and the range of the historical super-Lévy process.
<正> In this paper,we introduce a class of Gaussian processes Y={Y(t):t∈R_+~N},the so called bi-fractional Brownian motion with the indexes H-(H_1,…,H_N)and α.We consider the(N,d,H,α)Gaussianrandom fieldX(t)=(X_1(t),…,X_d(t)),where X_1(t),…,X_d(t)are independent copies of Y(t).At first we show the existence and join continuity of thelocal times of X={X(t),t∈R_+~N},then we consider the Hlder conditions for the local times.
