Estimation of the drift function for Ito processes and a class of semimartingales via histogram sieve

Volume 33 / 2006

Roman Ró/za/nski, Adam Zagda/nski Applicationes Mathematicae 33 (2006), 21-40 MSC: Primary 62M09; Secondary 62G05. DOI: 10.4064/am33-1-2

Abstract

A histogram sieve estimator of the drift function in Ito processes and some semimartingales is constructed. It is proved that the estimator is pointwise and $L^{1}$ consistent and its finite-dimensional distributions are asymptotically normal. Our approach extends the results of Leśkow and Różański (1989a).

Authors

  • Roman Ró/za/nskiInstitute of Mathematics and Computer Science
    Wroc/law University of Technology
    Wybrzeże Wyspia/nskiego 27
    50-370 Wroc/law, Poland
    e-mail
  • Adam Zagda/nskiInstitute of Mathematics and Computer Science
    Wroc/law University of Technology
    Wybrzeże Wyspia/nskiego 27
    50-370 Wroc/law, Poland

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