Ehsan Azmoodeh - Optimal Variance–Gamma Approximation on Wiener Space
|Dates:||2 December 2020|
|Times:||15:00 - 15:00|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
|Speaker:||, , Sebastian Andres|
Ehsan Azmoodeh (Liverpool) will speak in the Probability seminar.
In this talk, we consider the problem of optimal Variance-Gamma approximation on Wiener space in terms of a suitable integral probability metric. On the second Wiener chaos, we demonstrate a non-asymptotic optimal quantitative rate in terms of maximum of the first six cumulants. Our result extends the celebrated optimal fourth moment theorem due to Nourdin & Peccati (Proc. Amer. Math. Soc.,143(7):3123–3133, 2015) for normal approximation. The main body of our analysis constitutes of the following techniques: (i) Malliavin calculus on Wiener space (ii) a splitting technique for test functions in the Lipschitz Banach space relying on the compactness of the Stein operator (iii) recent development of Stein method for Variance–Gamma distribution due to Robert Gaunt (https://arxiv.org/abs/2008.06088, 2020). As an application, we illustrate the optimal rate 1/n improved by a power two of convergence for the generalized Rosenblatt process at extreme critical exponent due to Bai & Taqqu (Ann. Probab. 45, 1278–1324, 2017).
This is a joint work in progress with Peter Eichelsbacher and Christoph Thäle at Ruhr University Bochum.
Organisation: University of Liverpool
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