This work is the fruit of recent advances concerning both nonparametric statistical modelling
and functional variables and is based on various publications in international statistical …

Abstract Theory of random processes needs a kind of normal distribution. This is why
Gaussian vectors and Gaussian distributions in infinite-dimensional spaces come into play …

We find the exact small deviation asymptotics for the L 2-norm of various m-times integrated
Gaussian processes closely connected with the Wiener process and the Ornstein …

Abstract We establish a Karhunen-Loève expansion for generic centered, second order
stochastic processes, which does not rely on topological assumptions. We further investigate …

We find the logarithmic $ L_2 $-small ball asymptotics for a large class of zero mean
Gaussian fields with covariances having the structure of “tensor product”. The main condition …

We will introduce a class of m-times integrated Brownian motions. The exact asymptotic
expansions for the $ L_2 $-small ball probabilities will be discussed for members of this …

We sharpen a classical result on the spectral asymptotics of boundary-value problems for
self-adjoint ordinary differential operator. Using this result, we obtain the exact L 2-small ball …

In this paper we consider the Laplace transforms of some random series, in particular, the
random series derived as the squared L_2 norm of a Gaussian stochastic process. Except …

Motivated by asymptotic problems in the theory of empirical processes, and specifically by
tests of independence, we study the law of quadratic functionals of the (weighted) Brownian …

L2-small ball asymptotics for Gaussian random functions: A survey Page 1 Probability Surveys
Vol. 20 (2023) 608–663 ISSN: 1549-5787 https://doi.org/10.1214/23-PS20 L2-small ball …