Speaker: Riccardo Passeggeri, Imperial College London
Abstract: In this talk I will present the mathematics and the statistics developed to study high-frequency phenomena. The talk is accessible to students. I will give a general overview of the problem and its applications, which are mainly in turbulences and finance. Then, I will introduce the main mathematical object of the talk: the Brownian semistationary (BSS) process. The BSS process is an extension of the moving average process. The results are divided into two parts. First, I will present a central limit theorem for general stationary Gaussian processes. Then, I will present limit theorems and feasible results for BSS processes. I will conclude the talk by explaining how these results are crucial for our understanding of high-frequency phenomena and I will provide a practical example.