We study numerical integration of Lipschitz functionals on a Banach space by means of
deterministic and randomized (Monte Carlo) algorithms. This quadrature problem is shown …

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 …

We present a fully constructive method for quantization of the solution X of a scalar SDE in
the path space L p [0, 1] or C [0, 1]. The construction relies on a refinement strategy which …

1. Введение. Пятидесятые и шестидесятые годы XX века были годами особого
творческого подъема АН Колмогорова, и его работы тех лет тесно связаны с теорией …

For n∈ N, r∈(0,∞) and a Radon random vector X with values in a Banach space E let en, r
(X, E)= inf (Emina∈ α∥ Xa∥ r) 1/r, where the infimum is taken over all subsets α of E with …

We present a survey of results on minimal errors and optimality of algorithms for strong and
weak approximation of systems of stochastic differential equations. For strong …

For a broad class of Banach spaces with Gaussian measure, we show that their entropy in
the sense of Shannon (the mm-entropy) is closely related to the entropy of the …

We survey recent results on numerical integration with respect to measures μ on infinite-
dimensional spaces, eg, Gaussian measures on function spaces or distributions of diffusion …

We establish the precise asymptotics of the quantization and entropy coding errors for
fractional Brownian motion with respect to the supremum norm and L^p0,1-norm distortions …

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 …