An invariance principle in $L^2[0,1]$ for non stationary $\varphi $-mixing sequences

Paulo Eduardo Oliveira; Charles Suquet

Displaying similar documents to “An invariance principle in $L^{2} [0, 1]$ for non stationary $ϕ$ -mixing sequences”

An $L^{2} [0, 1]$ invariance principle for LPQD random variables.

Oliveira, P.E., Suquet, Ch. (1996)

Portugaliae Mathematica

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Limit theorems for U-statistics indexed by a one dimensional random walk

Nadine Guillotin-Plantard, Véronique Ladret (2005)

ESAIM: Probability and Statistics

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Let ${(S_{n})}_{n \geq 0}$ be a $ℤ$ -random walk and ${(ξ_{x})}_{x \in ℤ}$ be a sequence of independent and identically distributed $ℝ$ -valued random variables, independent of the random walk. Let $h$ be a measurable, symmetric function defined on $ℝ^{2}$ with values in $ℝ$ . We study the weak convergence of the sequence $𝒰_{n}, n \in ℕ$ , with values in $D [0, 1]$ the set of right continuous real-valued functions with left limits, defined by $\sum_{i, j = 0}^{[n t]} h (ξ_{S_{i}}, ξ_{S_{j}}), t \in [0, 1] .$ Statistical applications are presented, in particular we prove a strong law of large numbers for...

Central limit theorem for sampled sums of dependent random variables

Nadine Guillotin-Plantard, Clémentine Prieur (2010)

ESAIM: Probability and Statistics

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We prove a central limit theorem for linear triangular arrays under weak dependence conditions. Our result is then applied to dependent random variables sampled by a $ℤ$ -valued transient random walk. This extends the results obtained by [N. Guillotin-Plantard and D. Schneider, (2003) 477–497]. An application to parametric estimation by random sampling is also provided.

Complete convergence of weighted sums for arrays of rowwise $ϕ$ -mixing random variables

Xinghui Wang, Xiaoqin Li, Shuhe Hu (2014)

Applications of Mathematics

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In this paper, we establish the complete convergence and complete moment convergence of weighted sums for arrays of rowwise $ϕ$ -mixing random variables, and the Baum-Katz-type result for arrays of rowwise $ϕ$ -mixing random variables. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequences of $ϕ$ -mixing random variables is obtained. We extend and complement the corresponding results of X. J. Wang, S. H. Hu (2012).

On the existence and asymptotic behavior of the random solutions of the random integral equation with advancing argument

Henryk Gacki (1996)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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1. Introduction Random Integral Equations play a significant role in characterizing of many biological and engineering problems [4,5,6,7]. We present here new existence theorems for a class of integral equations with advancing argument. Our method is based on the notion of a measure of noncompactness in Banach spaces and the fixed point theorem of Darbo type. We shall deal with random integral equation with advancing argument $x (t, ω) = h (t, ω) + \int^{t + δ (t)} ₀ k (t, τ, ω) f (τ, x_{τ} (ω)) d τ$ , (t,ω) ∈ R⁺ × Ω, (1) where (i) (Ω,A,P) is a complete probability...

Ballistic regime for random walks in random environment with unbounded jumps and Knudsen billiards

Francis Comets, Serguei Popov (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We consider a random walk in a stationary ergodic environment in $ℤ$ , with unbounded jumps. In addition to uniform ellipticity and a bound on the tails of the possible jumps, we assume a condition of strong transience to the right which implies that there are no “traps.” We prove the law of large numbers with positive speed, as well as the ergodicity of the environment seen from the particle. Then, we consider Knudsen stochastic billiard with a drift in a random tube in $ℝ^{d}$ , $d \geq 3$ , which serves...

Complete $q$ -order moment convergence of moving average processes under $ϕ$ -mixing assumptions

Xing-Cai Zhou, Jin-Guan Lin (2014)

Applications of Mathematics

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Let ${Y_{i}, - \infty < i < \infty}$ be a doubly infinite sequence of identically distributed $ϕ$ -mixing random variables, and ${a_{i}, - \infty < i < \infty}$ an absolutely summable sequence of real numbers. We prove the complete $q$ -order moment convergence for the partial sums of moving average processes $\{X_{n} = \sum_{i = - \infty}^{\infty} a_{i} Y_{i + n}, n \geq 1\}$ based on the sequence ${Y_{i}, - \infty < i < \infty}$ of $ϕ$ -mixing random variables under some suitable conditions. These results generalize and complement earlier results.

Strong laws of large numbers for arrays of rowwise $ρ^{*}$ -mixing random variables.

Zhu, Meng-Hu (2007)

Discrete Dynamics in Nature and Society

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Displaying similar documents to “An invariance principle in L 2 [ 0 , 1 ] for non stationary ϕ -mixing sequences”

Displaying similar documents to “An invariance principle in $L^{2} [0, 1]$ for non stationary $ϕ$ -mixing sequences”