[图书][B] Nonparametric functional data analysis
F Ferraty - 2006 - Springer
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 …
and functional variables and is based on various publications in international statistical …
[图书][B] Lectures on Gaussian processes
M Lifshits, M Lifshits - 2012 - Springer
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 …
Gaussian vectors and Gaussian distributions in infinite-dimensional spaces come into play …
[图书][B] Karhunen-Loeve expansions and their applications
L Wang - 2008 - search.proquest.com
Abstract The Karhunen-Loeve Expansion (KL expansion) is a bi-orthogonal stochastic
process expansion. In the field of stochastic process, the Karhunen-Loeve expansion …
process expansion. In the field of stochastic process, the Karhunen-Loeve expansion …
[HTML][HTML] Proof techniques in quasi-Monte Carlo theory
J Dick, A Hinrichs, F Pillichshammer - Journal of Complexity, 2015 - Elsevier
In this survey paper we discuss some tools and methods which are of use in quasi-Monte
Carlo (QMC) theory. We group them in chapters on Numerical Analysis, Harmonic Analysis …
Carlo (QMC) theory. We group them in chapters on Numerical Analysis, Harmonic Analysis …
Exact L 2 -small ball behavior of integrated Gaussian processes and spectral asymptotics of boundary value problems
AI Nazarov, YY Nikitin - Probability Theory and Related Fields, 2004 - Springer
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 …
Gaussian processes closely connected with the Wiener process and the Ornstein …
Sharp asymptotics of the functional quantization problem for Gaussian processes
H Luschgy, G Pagès - 2004 - projecteuclid.org
SHARP ASYMPTOTICS OF THE FUNCTIONAL QUANTIZATION PROBLEM FOR GAUSSIAN
PROCESSES Universität Trier and Université Paris 6 1. In Page 1 The Annals of Probability …
PROCESSES Universität Trier and Université Paris 6 1. In Page 1 The Annals of Probability …
Convergence types and rates in generic Karhunen-Loeve expansions with applications to sample path properties
I Steinwart - Potential Analysis, 2019 - Springer
Abstract We establish a Karhunen-Loève expansion for generic centered, second order
stochastic processes, which does not rely on topological assumptions. We further investigate …
stochastic processes, which does not rely on topological assumptions. We further investigate …
Small ball probabilities for Gaussian random fields and tensor products of compact operators
A Karol, A Nazarov, Y Nikitin - Transactions of the American Mathematical …, 2008 - ams.org
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 …
Gaussian fields with covariances having the structure of “tensor product”. The main condition …
[图书][B] Marginal and functional quantization of stochastic processes
H Luschgy, G Pagès - 2023 - Springer
Vector Quantization is the name given to discretization methods based on nearest
neighbour search. It was developed in the 1950s, mostly in signal processing and …
neighbour search. It was developed in the 1950s, mostly in signal processing and …
Laplace transforms via Hadamard factorization
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 …
random series derived as the squared L_2 norm of a Gaussian stochastic process. Except …