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

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Keywords

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