Geodesic
A functional limit theorem for random variables with strong residual dependence
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 813-832

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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. 
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     author = {O. V. Rusakov},
     title = {A functional limit theorem for random variables with strong residual dependence},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {813--832},
     publisher = {mathdoc},
     volume = {40},
     number = {4},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a7/}
}
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O. V. Rusakov. A functional limit theorem for random variables with strong residual dependence. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 813-832. http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a7/