This article is cited in 2 papers

A functional limit theorem for random variables with strong residual dependence

O. V. Rusakov

St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: To describe a certain model of strongly dependent noise, we introduce the scheme of summation of independent random variables with random replacements. The scheme generates a strictly stationary Markov sequence of random variables. We say that random variables from this sequence have “residual dependence.” In the paper, a Kolmogorov-type inequality for elements of this sequence is given. A functional limit theorem is proved for random polygons generated by these elements. The limiting process turns out to be an Ornstein–Uhlenbeck process.

Keywords: strong dependence, functional limit theorem, Ornstein–Uhlenbeck process, Gaussian noise model.

Received: 15.06.1993

 English version: Theory of Probability and its Applications, 1995, 40:4, 714–728

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