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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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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