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On the increments of a $d$-dimensional Gaussian process
Zhengyan Lin,황교신 대한수학회 2005 대한수학회지 Vol.42 No.6
In this paper we establish some results on the increments of a $d$-dimensional Gaussian process with the usual Euclidean norm. In particular we obtain the law of iterated logarithm and the Book-Shore type theorem for the increments of a $d$-dimensional Gaussian process, via estimating upper bounds and lower bounds of large deviation probabilities on the suprema of the $d$-dimensional Gaussian process.
ON THE INCREMENTS OF A d-DIMENSIONAL GAUSSIAN PROCESS
LIN ZHENGYAN,HWANG KYO-SHIN Korean Mathematical Society 2005 대한수학회지 Vol.42 No.6
In this paper we establish some results on the increments of a d-dimensional Gaussian process with the usual Euclidean norm. In particular we obtain the law of iterated logarithm and the Book-Shore type theorem for the increments of ad-dimensional Gaussian process, via estimating upper bounds and lower bounds of large deviation probabilities on the suprema of the d-dimensional Gaussian process.
Strassen's functional LIL for $d$-dimensional self-similar Gaussian process in H\"older norm
황교신,Zhengyan Lin 대한수학회 2005 대한수학회지 Vol.42 No.5
In this paper, based on largedeviation probabilities on Gaussian random vectors, we obtainStrassen's functional LIL for d-dimensional self-similarGaussian process in H"older norm via estimating large deviationprobabilities for d-dimensional self-similar Gaussian process in H\"older norm.
Limit behaviors for the increments of a $d-$dimensional multi-parameter Gaussian process
최용갑,Zhengyan Lin,황교신,문희진,성화상 대한수학회 2005 대한수학회지 Vol.42 No.6
In this paper, we establish limit theorems containing both the moduli of continuity and the large incremental results for finite dimensional Gaussian processes with $N$ parameters, via estimating upper bounds of large deviation probabilities on suprema of the Gaussian processes.
STRASSEN'S FUNCTIONAL LIL FOR d-DIMENSIONAL SELF-SIMILAR GAUSSIAN PROCESS IN HOLDER NORM
HWANG, KYO-SHIN,LIN, ZHENGYAN Korean Mathematical Society 2005 대한수학회지 Vol.42 No.5
In this paper, based on large deviation probabilities on Gaussian random vectors, we obtain Strassen's functional LIL for d-dimensional self-similar Gaussian process in Holder norm via estimating large deviation probabilities for d-dimensional self-similar Gaussian process in Holder norm.