Hauptmenü
  • Autor
    • Berkes, István
    • Liu, Weidong
    • Wu, Wei Biao
  • TitelKomlós-Major-Tusnády approximation under dependence
  • Volltext
  • DOI10.1214/13-AOP850
  • Persistent Identifier
  • Erschienen inThe Annals of Probability
  • Band42
  • Erscheinungsjahr2014
  • Heft2
  • Seiten794-817
  • LicenceCC BY
  • ISSN2168-894X
  • ZugriffsrechteCC-BY
  • Download Statistik50
  • Peer ReviewJa
  • AbstractThe celebrated results of Komlós, Major and Tusnády (1975, 1976) give optimal Wiener approximation for the partial sums of i.i.d. random variables and provide a powerful tool in probability and statistics. In this paper we extend KMT approximation for a large class of dependent stationary processes, solving a long standing open problem in probability theory. Under the framework of stationary causal processes and functional dependence measures of Wu (2005), we show that, under natural moment conditions, the partial sum processes can be approximated by Wiener process with an optimal rate. Our dependence conditions are mild and easily verifiable. The results are applied to ergodic sums, as well as to nonlinear time series and Volterra processes, an important class of nonlinear processes.