Related papers: On a novel probabilistic Sampling Kantorovich oper…
This paper studies approximation properties of linear sampling operators in general Banach lattices $X$. We obtain matching direct and inverse approximation estimates, convergence criteria, equivalence results involving special…
The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…
A popular approach to solving large probabilistic systems relies on aggregating states based on a measure of similarity. Many approaches in the literature are heuristic. A number of recent methods rely instead on metrics based on the notion…
In this paper, we describe two novel changes to the Baskakov-Durrmeyer operators that improve their approximation performance. These improvements are especially designed to produce higher rates of convergence, with orders of one or two.…
In this paper, we consider the problem of approximating the spectral distribution for a class of random operators over sofic groups. For this purpose, we make use of the concept of locally and empirically converging measures defined by…
Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…
In this paper, we introduce a Kantorovich type generalization of Jakimovski-Leviatan operators constructed by A. Jakimovski and D. Leviatan (1969) and the theorems on convergence and the degrree of convergence are established. Furthermore,…
We introduce symplectic quantization, a novel functional approach to quantum field theory which allows to sample quantum fields fluctuations directly in Minkowski space-time, at variance with the traditional importance sampling protocols,…
We develop a stochastic integration theory for predictable integrands with respect to a L\'evy basis. Our approach is based on decoupling inequalities for tangent sequences and reduces the construction of the stochastic integral essentially…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using It\^o's formula and on a new…
In this paper, we introduce a Stancu-type generalization of multivariate neural network operators by incorporating two parameters that perturb the sampling nodes. The proposed operators extend the existing neural network operator by…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
Our main purpose of this article is to study the convergence and other related properties of q-Bernstein-Kantorovich operators including the shifted knots of real positive numbers. We design the shifted knots of Bernstein-Kantorovich…
We establish quantitative estimates for sampling (dominating) sets in model spaces associated with meromorphic inner functions, i.e. those corresponding to de Branges spaces. Our results encompass the Logvinenko-Sereda-Panejah (LSP) Theorem…
Sensitivity properties describe how changes to the input of a program affect the output, typically by upper bounding the distance between the outputs of two runs by a monotone function of the distance between the corresponding inputs. When…
In this paper, we considered the problem of the simultaneous approximation of a function and its derivatives by means of the well-known neural network (NN) operators activated by sigmoidal function. Other than a uniform convergence theorem…
Starting with an operator in the universal enveloping algebra of a semi-simple, complex Lie group the nearest neighbor statistics of the spectra of this operator along a sequence of representations are discussed. After a short introduction…
In this paper we present a variant of the well known Skorokhod Representation Theorem. In our main result, given $S$ a Polish space, to a given continous path $\alpha$ in the space of probability measures on $S$, we associate a continuous…
We formulate both Markov chain Monte Carlo (MCMC) sampling algorithms and basic statistical physics in terms of elementary symmetries. This perspective on sampling yields derivations of well-known MCMC algorithms and a new parallel…