The maximal variation of a bounded martingale and the central limit theorem
Bernard De Meyer (1998)
Annales de l'I.H.P. Probabilités et statistiques
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Bernard De Meyer (1998)
Annales de l'I.H.P. Probabilités et statistiques
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B. Rajeev, M. Yor (1995)
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Liming Wu (1999)
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Albert Badrikian, Ali Süleyman Üstünel (1996)
Annales mathématiques Blaise Pascal
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Claude Martini (2000)
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Studia Mathematica
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Necessary and sufficient conditions are found for the exponential Orlicz norm (generated by with 0 < p ≤ 2) of or to be finite, where is a standard Brownian motion and τ is a stopping time for B. The conditions are in terms of the moments of the stopping time τ. For instance, we find that as soon as for some constant C > 0 as k → ∞ (or equivalently ). In particular, if τ ∼ Exp(λ) or then the last condition is satisfied, and we obtain with some universal constant...