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Continuous Ocone Martingales as Weak Limits of Rescaled Martingales

   
@article{ECP1062,
	author = {Harry Zanten},
	title = {Continuous Ocone Martingales as Weak Limits of Rescaled Martingales},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {7},
	year = {2002},
	keywords = {},
	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.},
	pages = {no. 21, 215-222},
	issn = {1083-589X},
	doi = {10.1214/ECP.v7-1062},    
        url = {http://ecp.ejpecp.org/article/view/1062}}