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Komlós-Major-Tusnády approximation under dependence. (English) Zbl 1308.60037
The authors of the paper analyze the Komlós-Major-Tusnády (KMT) approximation. They note that the dyadic construction of J. Komlós et al. [Z. Wahrscheinlichkeitstheor. Verw. Geb. 32, 111–131 (1975; Zbl 0308.60029); ibid. 34, 33–58 (1976; Zbl 0307.60045)] is highly technical and utilizes conditional large deviation techniques, which makes it very difficult to extend to dependent processes. So, the authors develop a new approximation technique, called triadic decomposition scheme, that enables them to prove the KMT approximation for all \(p >2\) and a large class of dependent sequences under natural moment conditions. Also, the authors give a few examples of applications to ergodic sums, nonlinear time series and Volterra processes.

MSC:
60F17 Functional limit theorems; invariance principles
60G10 Stationary stochastic processes
60J65 Brownian motion
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