Komlós-Major-Tusnády approximation under dependence
The authors of the paper analyze the Komlós-Major-Tusnády (KMT) approximation. They note that the dyadic construction of \textit{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.
scientific article