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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

Limit Theorems for a Class of Additive Functionals of Symmetric Stable Process and Fractional Brownian Motion in Besov-Orlicz Spaces

M. Ait Ouahra1, A. Kissami1 and A. Sghir1
  • 1 , Morocco

Abstract

We use the Potter's Theorem and the tightness criterion in Besov-Orlicz spaces, recently proved, to generalize some limit theorem for occupation times problem of certain self-similar process, namely symmetric stable process of index 1<α≤ and fractional Brownian motion of Hurst parameter 0<H<1. We give also strong approximation version of our limit theorem, more precisely, we show Lp-estimate version.

Journal of Mathematics and Statistics
Volume 8 No. 4, 2012, 506-516

DOI: https://doi.org/10.3844/jmssp.2012.506.516

Submitted On: 20 October 2012 Published On: 22 February 2013

How to Cite: Ouahra, M. A., Kissami, A. & Sghir, A. (2012). Limit Theorems for a Class of Additive Functionals of Symmetric Stable Process and Fractional Brownian Motion in Besov-Orlicz Spaces. Journal of Mathematics and Statistics, 8(4), 506-516. https://doi.org/10.3844/jmssp.2012.506.516

Open AccessCopyright: © 2012 M. Ait Ouahra, A. Kissami and A. Sghir. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Besov-Orlicz Spaces
  • Limit Theorems
  • Strong Approximation
  • Selfsimilar Process
  • Fractional Derivative
  • Additive Functional
  • Regularly Varying Function