The Annals of Probability

Strong Limit Theorems for Large and Small Increments of $l^p$-Valued Gaussian Processes

Miklos Csorgo and Qi-Man Shao

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Abstract

Based on the well-known Borell inequality and on a general theorem for large and small increments of Banach space valued stochastic processes of Csaki, Csorgo and Shao, we establish some almost sure path behaviour of increments in general, and moduli of continuity in particular, for $l^p$-valued, $1 \leq p < \infty$, Gaussian processes with stationary increments. Applications to $l^p$-valued fractional Wiener and Ornstein-Uhlenbeck processes are also discussed. Our results refine and extend those of Csaki, Csorgo and Shao.

Article information

Source
Ann. Probab., Volume 21, Number 4 (1993), 1958-1990.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989007

Digital Object Identifier
doi:10.1214/aop/1176989007

Mathematical Reviews number (MathSciNet)
MR1245297

Zentralblatt MATH identifier
0791.60028

JSTOR
links.jstor.org

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60G10: Stationary processes 60G17: Sample path properties 60F15: Strong theorems 60G07: General theory of processes 60F10: Large deviations

Keywords
Banach space valued processes $l^p$-valued Gaussian fractional Wiener and Ornstein-Uhlenbeck processes path properties large increments and moduli of continuity

Citation

Csorgo, Miklos; Shao, Qi-Man. Strong Limit Theorems for Large and Small Increments of $l^p$-Valued Gaussian Processes. Ann. Probab. 21 (1993), no. 4, 1958--1990. doi:10.1214/aop/1176989007. https://projecteuclid.org/euclid.aop/1176989007


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