Do, 08.02.2018, 16:15
Exact L_2-small ball probabilities for finite-dimensional perturbations of Gaussian processes: spectral method
Oberseminar AG Stochastik

Referent: Yulia Petrova, University St. Petersburg
Raum: S2|15 Raum 401

I consider the problem of small ball probabilities for Gaussian processes in L_2-norm. I focus on the processes which are important in
statistics (e.g. Kac-Kiefer-Wolfowitz processes), which are finite dimentional perturbations of Gaussian processes.  Depending on the properties of the kernel and perturbation matrix I consider two cases: non-critical and critical.For non-critical case I prove the general theorem for precise asymptotics of small deviations.For a huge class of critical processes I prove a general theorem in the same spirit as for
non-critical processes, but technically much more difficult.  At the same time a lot of
processes naturally appearing in statistics (e.g. Durbin, detrended processes) are not covered by those general theorems, so I treat them separately using methods of spectral theory and complex analysis.



Fachbereich Mathematik
Technische Universität Darmstadt

Schlossgartenstraße 7
64289 Darmstadt

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