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Continuous Ocone Martingales as Weak Limits of Rescaled Martingales
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Harry van Zanten, Vrije Universiteit Amsterdam
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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.
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Full text: PDF
Pages: 215-222
Published on: November 28, 2002
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Electronic Communications in Probability. ISSN: 1083-589X |
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