scholarly journals The Law of the Iterated Logarithm on Arbitrary Sequences for Stationary Gaussian Processes and Brownian Motion

1977 ◽  
Vol 5 (5) ◽  
pp. 724-739 ◽  
Author(s):  
Clifford Qualls
Keyword(s):  
Brownian Motion ◽  
Gaussian Processes ◽  
And Brownian Motion ◽  
Iterated Logarithm ◽  
The Law ◽  
Stationary Gaussian Processes

Weak approximation for a class of Gaussian processes

2000 ◽  
Vol 37 (02) ◽  
pp. 400-407 ◽  
Author(s):  
Rosario Delgado ◽  
Maria Jolis
Keyword(s):  
Brownian Motion ◽  
Poisson Process ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Stochastic Integral ◽  
Hurst Parameter ◽  
Standard Wiener Process ◽  
Weak Approximation ◽  
The Law ◽  
Continuous Gaussian Process

We prove that, under rather general conditions, the law of a continuous Gaussian process represented by a stochastic integral of a deterministic kernel, with respect to a standard Wiener process, can be weakly approximated by the law of some processes constructed from a standard Poisson process. An example of a Gaussian process to which this result applies is the fractional Brownian motion with any Hurst parameter.

The law of the iterated logarithm for Brownian sheets

1975 ◽  
Vol 12 (4) ◽  
pp. 840-844
Author(s):  
W. J. Park
Keyword(s):  
Banach Space ◽  
Brownian Motion ◽  
Iterated Logarithm ◽  
The Law

Strassen-type law of the iterated logarithm for Brownian sheets presented by Pyke [7] is proved by using recent results of Kuelbs and Lepage [4]: the law of the iterated logarithm for Brownian motion in a Banach space and some applications are given.

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