Convergence rates for regularized optimal transport via quantization
S Eckstein, M Nutz - Mathematics of Operations Research, 2024 - pubsonline.informs.org
We study the convergence of divergence-regularized optimal transport as the regularization
parameter vanishes. Sharp rates for general divergences including relative entropy or Lp …
parameter vanishes. Sharp rates for general divergences including relative entropy or Lp …
Vlasov equations on digraph measures
Many science phenomena are described as interacting particle systems (IPS). The mean
field limit (MFL) of large all-to-all coupled deterministic IPS is given by the solution of a PDE …
field limit (MFL) of large all-to-all coupled deterministic IPS is given by the solution of a PDE …
Mean field limits of co-evolutionary heterogeneous networks
Many science phenomena are modelled as interacting particle systems (IPS) coupled on
static networks. In reality, network connections are far more dynamic. Connections among …
static networks. In reality, network connections are far more dynamic. Connections among …
[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 …
Uniform decomposition of probability measures: quantization, clustering and rate of convergence
J Chevallier - Journal of Applied Probability, 2018 - cambridge.org
The study of finite approximations of probability measures has a long history. In Xu and
Berger (2017), the authors focused on constrained finite approximations and, in particular …
Berger (2017), the authors focused on constrained finite approximations and, in particular …
Circling the uniform distribution
A Berger, A Rahmatidehkordi - Journal of Mathematical Analysis and …, 2023 - Elsevier
Distributions modulo one of slowly varying sequences are of wide interest in analysis and
number theory. For every real sequence (xn) for which lim n→∞ n (x n+ 1− xn) exists, this …
number theory. For every real sequence (xn) for which lim n→∞ n (x n+ 1− xn) exists, this …
Random bit quadrature and approximation of distributions on Hilbert spaces
We study the approximation of expectations E (f (X)) E (f (X)) for Gaussian random elements
X with values in a separable Hilbert space H and Lipschitz continuous functionals f: H → R f …
X with values in a separable Hilbert space H and Lipschitz continuous functionals f: H → R f …
Lattice approximations in wasserstein space
K Hamm, V Khurana - arXiv preprint arXiv:2310.09149, 2023 - arxiv.org
We consider structured approximation of measures in Wasserstein space $ W_p (\mathbb
{R}^ d) $ for $ p\in [1,\infty) $ by discrete and piecewise constant measures based on a …
{R}^ d) $ for $ p\in [1,\infty) $ by discrete and piecewise constant measures based on a …
Approximation rate in Wasserstein distance of probability measures on the real line by deterministic empirical measures
O Bencheikh, B Jourdain - Journal of Approximation Theory, 2022 - Elsevier
We are interested in the approximation in Wasserstein distance with index ρ≥ 1 of a
probability measure μ on the real line with finite moment of order ρ by the empirical measure …
probability measure μ on the real line with finite moment of order ρ by the empirical measure …
[HTML][HTML] Random bit multilevel algorithms for stochastic differential equations
We study the approximation of expectations E (f (X)) for solutions X of SDEs and functionals
f: C ([0, 1], R r)→ R by means of restricted Monte Carlo algorithms that may only use random …
f: C ([0, 1], R r)→ R by means of restricted Monte Carlo algorithms that may only use random …