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Occupation time problems for fractional Brownian motion and some other self-similar processes
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M. Ait Ouahra
Published/Copyright:
May 29, 2009
Abstract
In this paper, we study the regularity of the fractional derivative of the local time of some self-similar processes and we establish limit theorems for occupation time problems for a class of self-similar processes. Finally, we get the strong approximation analogues of our limit theorems. Fractional derivative and Hilbert transform of the local time of self-similar processes are limits of occupation time problems.
Key words.: Fractional Brownian motion; self-similar process; limit theorem; fractional derivative, Hilbert transform; local time; strong approximation
Received: 2008-03-06
Published Online: 2009-05-29
Published in Print: 2009-May
© de Gruyter 2009
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Keywords for this article
Fractional Brownian motion;
self-similar process;
limit theorem;
fractional derivative, Hilbert transform;
local time;
strong approximation
Articles in the same Issue
- Semicircle law for random matrices of long-range percolation model
- The stochastic maximum principle in optimal control of degenerate diffusions with non-smooth coefficients
- The asymptotic behaviour of the maximum of a random sample subject to trends in location and scale
- Evolution process as an alternative to diffusion process and Black–Scholes Formula
- Occupation time problems for fractional Brownian motion and some other self-similar processes
- Properties of the distribution of the random variable defined by A2-continued fraction with independent elements
