Convergence of dependent walks in a random scenery to fBm-local time fractional stable motionsReport as inadecuate




Convergence of dependent walks in a random scenery to fBm-local time fractional stable motions - Download this document for free, or read online. Document in PDF available to download.

1 IMT - Institut de Mathématiques de Toulouse UMR5219 2 LMA-Poitiers - Laboratoire de Mathématiques et Applications

Abstract : It is classical to approximate the distribution of fractional Brownian motion by a renormalized sum $ S n $ of dependent Gaussian random variables. In this paper we consider such a walk $ Z n $ that collects random rewards $ \xi j $ for $ j \in \mathbb Z,$ when the ceiling of the walk $ S n $ is located at $ j.$ The random reward or scenery $ \xi j $ is independent of the walk and with heavy tail. We show the convergence of the sum of independent copies of $ Z n$ suitably renormalized to a stable motion with integral representation, whose kernel is the local time of a fractional Brownian motion fBm. This work extends a previous work where the random walk $ S n$ had independent increments limits.

Keywords : local times Key words: stable process self-similarity fractional Brownian motion random walk random scenery local times.





Author: Serge Cohen - Clément Dombry -

Source: https://hal.archives-ouvertes.fr/



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