Displaying similar documents to “Convergence of stopped sums of weakly dependent random variables.”

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).

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.

Exponential inequalities and functional central limit theorems for random fields

Jérôme Dedecker (2001)

ESAIM: Probability and Statistics

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We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform φ -mixing random fields, we require both finite fourth moments and an algebraic decay of the...