Study of the Convergence of the Increments of Gaussian Process

Abdelkader Bahram; Shaban A. El-Shehawy

doi:10.4236/am.2015.66085

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Applied Mathematics > Vol.6 No.6, June 2015

Study of the Convergence of the Increments of Gaussian Process ()

Abdelkader Bahram¹, Shaban A. El-Shehawy²

¹Department of Mathematics, Djillali Liabes University, Sidi Bel Abbès, Algeria.
²Department of Mathematics, Faculty of Science, Menoufia University, Shebin El-Kom, Egypt.

DOI: 10.4236/am.2015.66085 PDF HTML XML 3,644 Downloads 4,043 Views Citations

Abstract

Let

be a Gaussian process with stationary increments

. Let

be a nondecreasing function of t with

. This paper aims to study the almost sure behaviour of

where

with

and

is an increasing sequence diverging to

Keywords

Wiener Process, Gaussian Process, Law of the Iterated Logarithm, Regularly Varying Function

Share and Cite:

Bahram, A. and El-Shehawy, S. (2015) Study of the Convergence of the Increments of Gaussian Process. Applied Mathematics, 6, 933-939. doi: 10.4236/am.2015.66085.

Conflicts of Interest

The authors declare no conflicts of interest.

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