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In this paper, we introduce the notion of efficiency (consistency) and examine some asymptotic properties ofMarkov chain Monte Carlo methods. We apply these results to the Gibbs sampler for independen...
Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are continuous on certain subsets of the unit hy...
In this paper, we study the weak convergence of the integrated periodogram indexed by classes of functions for linear processes with symmetric $\alpha$-stable innovations. Under suitable summability ...
We study large deviation properties of systems of weakly interacting particles modeled by Itô stochastic differential equations (SDEs).It is known under certain conditions that the corresponding...
Let {Xn}n∈N be a sequence of i.i.d. randomvariables in Zd. Let Sk = X1 + ...+ Xk and Yn(t) be the continuous process on [0, 1] for which Yn(k/n) = Sk/√n k = 1, ..., n and which is linearly interpolate...
We establish the weak convergence of three-step Noor iterative scheme for an I-nonexpansive mappping in a Banach space which satisfies Opial’s condition. The presented results in this paper, is connec...
In this paper, we establish a Rosenthal-type inequality of the maximum of partial sums for $\rho^{-}$-mixing random fields. As its applications we get the H\'{a}jeck--R\`{e}nyi inequality and weak con...
In the present paper we prove that the mixing property of positive L1-contraction of finite von Neumann algebras implies the property of complete mixing.

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