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Study of the Convergence of the Increments of Gaussian Process
Department of Mathematics, Djillali Liabes University, Sidi Bel Abbès, Algeria
Department of Mathematics, Faculty of Science, Menoufia University, Shebin El-Kom, Egypt
- 1 Department of Mathematics, Djillali Liabes University, Sidi Bel Abbès, Algeria
- 2 Department of Mathematics, Faculty of Science, Menoufia University, Shebin El-Kom, Egypt
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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 .
KeywordsWiener ProcessGaussian ProcessLaw of the Iterated LogarithmRegularly Varying Function
- Bahram, A. (2014) Convergence of the Increments of a Wiener Process. Acta Mathematica Universitatis Comenianae, 83, 113-118.
- Hwang, K.S., Choi, Y.K. and Jung, J.S. (1997) On Superior Limits for the Increments of Gaussian Processes. Statistics and Probability Letters, 35, 289-296. http://dx.doi.org/10.1016/S0167-7152(97)00025-4
- Choi, Y.K. (1991) Erdös-Réyi Type Laws Applied to Gaussian Process. Journal of Mathematics of Kyoto University, 31, 191-217.
- Slepian, D. (1962) The One-Sided Barrier Problem for Gaussian Noise. Bell System Technical Journal, 41, 463-501. http://dx.doi.org/10.1002/j.1538-7305.1962.tb02419.x
- Vasudeva, R. and Savitha, S. (1993) On the Increments of Weiner Process—A Look through Subsequences. Stochastic Processes and Their Applications, 47, 153-158. http://dx.doi.org/10.1016/0304-4149(93)90101-9
- Fernique, X. (1975) Evaluations of Processus Gaussian Composes. Probability in Banach Spaces. Lecture Notes in Mathematics, 526, 67-83.