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On Wald’s equation. Discrete time case

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1655)

Abstract

Let m t be a square integrable martingale, m o =0, such that there exists limt→∞ m t =m a.s. We study a minimal possible sufficient condition for the validity of Wald’s equation Em =0 in terms of the tail behavior of a square characteristic S(m) of m t .

AMS 1991 classification

  • 60G42
  • 60G40

Key words

  • phrases
  • local martingale
  • Wald’s equation
  • uniform integrability
  • tauberian theorem

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© 1997 Springer-Verlag Berlin Heidelberg

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Galtchouk, L.I., Novikov, A.A. (1997). On Wald’s equation. Discrete time case. In: Azéma, J., Yor, M., Emery, M. (eds) Séminaire de Probabilités XXXI. Lecture Notes in Mathematics, vol 1655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0119299

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  • DOI: https://doi.org/10.1007/BFb0119299

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62634-3

  • Online ISBN: 978-3-540-68352-0

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