Edgeworth expansions for smooth functions of standardized subordinators via differential calculus for linear operators

• José A. Adell ^[1]
  1. [1] Universidad de Zaragoza

     Universidad de Zaragoza

     Zaragoza, España

     
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 2, Nº. 2, 2010, págs. 215-239
• Idioma: inglés
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• Resumen

  • We apply a differential calculus for linear operators, together with moduli of smoothness techniques, in order to obtain Edgeworth expansions for Eφ(Z(t)) − Eφ(Z), where (Z(t), t ≥ 1) is a standardized subordinator, Z is a standard normal random variable and φ is a suitable smooth function. The main achievement of the method is to provide explicit upper bounds for the remainders, thus getting rid off the ‘big or little o’ terms. Other features are the relative simplicity of the proofs and the property of monotonic convergence for Eφ(Z(t)) under simple sufficient conditions on φ.