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.
Citation
Harry Zanten. "Continuous Ocone Martingales as Weak Limits of Rescaled Martingales." Electron. Commun. Probab. 7 215 - 222, 2002. https://doi.org/10.1214/ECP.v7-1062
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