Related papers: Strongly mixed random errors in Mann's iteration a…
The article is devoted to the estimation of the rate of convergence of integral functionals of a Markov process. Under the assumption that the given Markov process admits a transition probability density which is differentiable in $t$ and…
We discuss conditions ensuring the (strict) convergence of stochastic gradient algorithms.
We prove a strong law of large numbers for a class of strongly mixing processes. Our result rests on recent advances in understanding of concentration of measure. It is simple to apply and gives finite-sample (as opposed to asymptotic)…
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic…
Estimating the mixing density of a mixture distribution remains an interesting problem in statistics literature. Using a stochastic approximation method, Newton and Zhang (1999) introduced a fast recursive algorithm for estimating the…
We describe the statistics of repetition times of a string of symbols in a stochastic process. Denote by T(A) the time elapsed until the process spells the finite string A and by S(A) the number of consecutive repetitions of A. We prove…
We provide in a unified way quantitative forms of strong convergence results for numerous iterative procedures which satisfy a general type of Fejer monotonicity where the convergence uses the compactness of the underlying set. These…
In this paper, we first define the concept of convexity in G-metric spaces. We then use Mann iterative process in this newly defined convex G-metric space to prove some convergence results for some classes of mappings. In this way, we can…
In many branches of engineering, Banach contraction mapping theorem is employed to establish the convergence of certain deterministic algorithms. Randomized versions of these algorithms have been developed that have proved useful in…
We study fast approximation of integrals with respect to stationary probability measures associated to iterated functions systems on the unit interval. We provide an algorithm for approximating the integrals under certain conditions on the…
In this paper, using the Bregman distance, we introduce a new projection-type algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points. Then the strong convergence of the sequence…
In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for…
This article aims to present the $AT$ algorithm, a novel two-step iterative approach for approximating fixed points of weak contractions within complete normed linear spaces. The article demonstrates the convergence of $AT$ algorithm…
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…
We study the almost sure convergence of randomly truncated stochastic algorithms. We present a new convergence theorem which extends the already known results by making vanish the classical condition on the noise terms. The aim of this work…
In this paper we estimate the expected error of a stochastic approximation algorithm where the maximum of a function is found using finite differences of a stochastic representation of that function. An error estimate of $O(n^{-1/5})$ for…
Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…
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 study functional type weak approximation of weak solutions of stochastic functional differential equations by means of the Euler--Maruyama scheme. Under mild assumptions on the coefficients, we provide a quantitative error…
In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…