For ad-dimensional random vector X, let pn, X (θ) be the probability that the convex hull of n
independent copies of X contains a given point θ. We provide several sharp inequalities …

In numerical integration, cubature methods are effective, especially when the integrands can
be well-approximated by known test functions, such as polynomials. However, the …

Given a probability measure μ on a set X and a vector-valued function φ, a common problem
is to construct a discrete probability measure on X such that the push-forward of these two …

This paper is an extended and reworked version of a short course given by the author
at''Uzbekistan-Ukrainian readings in stochastic processes'', Tashkent-Kyiv, 2022, and was …

Tchakaloff-like compression of QMC volume and surface integration on the union of balls |
Calcolo Skip to main content SpringerLink Account Menu Find a journal Publish with us Track …

Utilising classical results on the structure of Hopf algebras, we develop a novel approach for
the construction of cubature formulae on Wiener space based on unshuffle expansions. We …

The paper gives new results for the Milstein scheme of stochastic differential equations. We
show that (i) the Milstein scheme holds as a weak approximation in total variation sense and …

For a d-dimensional random vector X, let pn, X (θ) be the probability that the convex hull of n
independent copies of X contains a given point θ. We provide several sharp inequalities …

Discretization of probability measures is ubiquitous in the field of applied mathematics, from
classical numerical integration to data compression and algorithmic acceleration in machine …

Актуальность работы. Для описания динамических систем, состояние которых
изменяется в непрерывном времени, используются дифференциальные уравнения …