Séminaire SPACE Tours

Weak convergence to the maximum process of fractional Brownian motion with shot noise
Yizao Wang (University of Cincinnati)
Friday 23 May 2014 11:00 -  Tours -  Salle 1180 (Bât E2)

Résumé :
We consider the maximum process of a random walk with heavy-tailed noise. The random walk may have stationary increments, but its sample path is assumed to converge weakly to a fractional Brownian motion. When the largest noise has the same magnitude of the maxima of the random walk, we establish an invariance principle for the maximum process in the Skorohod topology. The limiting process is the maximum process of the fractional Brownian notion with shot noise generated by Poisson point processes. In this talk, we highlight the techniques of point process convergence, which is a standard tool for establishing limiting theorems involving random variables with regularly varying tails.

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