Functional Limit Theorems for d-dimensional FBM in H lder Norm

In this paper, we obtain functional limit theorems for d-dimensional FBM in HSlder norm via estimating large deviation probabilities for d-dimensional FBM in HSlder norm.

A LIL and Limit Distributions for Trimmed Sums of Random Vectors Attracted to Operator Semi-stable Laws

Let θ∈^d be a unit vector and let X, X1, X2,…… be a sequence of i.i.d. Xd-valued random vectors attracted to operator semi-stable laws. For each integer n ≥1, let X1,≤……≤ Xn,n denote the order statistics of X1, X2,..., Xn according to priority of index, namely ｜（X1,nθ）｜≥…≥ [（Xn,n,θ）1, where （., .） is an inner product on Rd. For all integers r ≥ 0, define by （r）Sn =∑n-r i=1Xi,n the trimmed sum. In this paper we investigate a law of the iterated logarithm and limit distributions for trimmed sums （r）Sn. Our results give information about the maximal growth rate of sample paths for partial sums of X when r extreme terms are excluded. A stochastically compactness of （r）Sn is obtained.

Asymptotic Distributions for Power Variation of the Solution to a Stochastic Heat Equation

Let u={u(t,x),t∈[0,T],x∈R}be a solution to a stochastic heat equation driven by a space-time white noise.We study that the realized power variation of the process u with respect to the time,properly normalized,has Gaussian asymptotic distributions.In particular,we study the realized power variation of the process u with respect to the time converges weakly to Brownian motion.

A Strong Approximation Theorem for Quasi-associated Sequences

By combining the Csorgo-Révész quantile transform methods and the Skorohod-Strassen martingale embedding theorem, we prove a strong approximation theorem for quasi-associated random variables with mean zero and finite （2 ＋ δ）th moment under polynomial decay rate. As a consequence, the decay rate for a strong approximation theorem of associated sequences of Yu （1996） is weakened.

On Global and Local Properties of the Trajectories of Gaussian Random Fields——A Look Through the Set of Limit Points

This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm at zero and infinity respectively.The sets of limit points of those Gaussian random fields are obtained.The main results are applied to fractional Riesz-Bessel processes and the sets of limit points of this field are obtained.

Chung-type Law of the Iterated Logarithm on l^p-valued Gaussian Processes

By estimating small ball probabilities for l^P-valued Gaussian processes, a Chung-type law of the iterated logarithm of l^P-valued Gaussian processes is given.