Asymptotic normality of the kernel estimate for the Markovian transition operator

Volume 38 / 2011

Samir Benaissa, Abbes Rabhi, Belaid Mechab Applicationes Mathematicae 38 (2011), 93-105 MSC: 62M05, 62M15. DOI: 10.4064/am38-1-7

Abstract

We build a kernel estimator of the Markovian transition operator as an endomorphism on $L^1$ for some discrete time continuous states Markov processes which satisfy certain additional regularity conditions. The main result deals with the asymptotic normality of the kernel estimator constructed.

Authors

  • Samir BenaissaLaboratoire de Mathématiques
    Université de Sidi Bel Abbes
    BP 89, Sidi Bel Abbes 22000, Algeria
    e-mail
  • Abbes RabhiLaboratoire de Mathématiques
    Université de Sidi Bel Abbes
    BP 89, Sidi Bel Abbes 22000, Algeria
    e-mail
  • Belaid MechabLMPM, Department of Mechanical Engineering
    University of Sidi Bel Abbes
    BP 89, Cité Ben M'hidi
    Sidi Bel Abbes 22000, Algeria

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