Continuous Ocone martingales as weak limits of rescaled martingales

J.H. Zanten, van

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    Abstract

    Consider a martingale $M$ with bounded jumps and two sequences $a_n, b_n to infty$. We show that if the rescaled martingales M^n_t =frac{1}{sqrt{a_n}}M_{b_n t} converge weakly, then the limit is necessarily a continous Ocone martingale. Necessary and sufficient conditions for the weak convergence of the rescaled martingales are also given.
    Original languageEnglish
    Pages (from-to)215-222
    JournalElectronic Communications in Probability
    Volume7
    Issue number21
    Publication statusPublished - 2002

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