Small ball probabilities for Gaussian Processes

Yulia Petrova · IMPA & Chebyshev Laboratory

2022-03-17 · 17:00 UTC-3

In the talk we will consider a problem of small ball probabilities for Gaussian processes, which consists in finding the asymptotics of probability that a norm of a process is less than $\epsilon$ as $\epsilon$ tends to zero. This question arises in different areas: quantization of Gaussian vectors, metric entropy, etc. We will consider what is already known in general situation and talk about more advanced results in $L_2$-norm, for which the distribution is totally defined by eigenvalues of the covariance operator.