Martin Raič: On the rate of the convergence in the multivariate central limit theorem with respect to the Wasserstein 1-distance

V torek, 24. 2. 2026, ob 16:15 bo v predavalnici 3.06 v okviru seminarja VeSFiM potekalo predavanje Martina Raiča z naslovom On the rate of the convergence in the multivariate central limit theorem with respect to the Wasserstein 1-distance.

Povzetek: Stein's method is known to be a powerful tool for estimation of the error in various versions and extensions of the central limit theorem. In the univariate case, it works very well for the Wasserstein 1-distance. This is due to the fact that the solution of the Stein equation is bounded for Lipschitz test functions. Unfortunately, the latter is not true in the multivariate case. This problem can be mitigated by smoothing, but direct approach reduces the estimated rate of convergence. In the case considered, it yields $ O(n^{-1/2} \log n) $ instead of expected $ O(n^{-1/2}) $. However, the undesired logarithmic factor can be removed by careful examination of the solution of the Stein equation, which is expressed in terms of the Ornstein-Uhlenbeck semigroup. The key idea is to use different expansions of the Stein operator depending on the outcome as well as the time in the Ornstein-Uhlenbeck process.

Predavanje bo potekalo v živo.

Vljudno vabljeni!