The Annals of Probability
- Ann. Probab.
- Volume 17, Number 2 (1989), 586-595.
Stopping Times and Tightness. II
To establish weak convergence of a sequence of martingales to a continuous martingale limit, it is sufficient (under the natural uniform integrability condition) to establish convergence of finite-dimensional distributions. Thus in many settings, weak convergence to a continuous limit process can be deduced almost immediately from convergence of finite-dimensional distributions. These results may be technically useful in simplifying proofs of weak convergence, particularly in infinite-dimensional settings. The results rely on a technical tightness condition involving stopping times and predictability of imminent jumps.
Ann. Probab., Volume 17, Number 2 (1989), 586-595.
First available in Project Euclid: 19 April 2007
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Aldous, David. Stopping Times and Tightness. II. Ann. Probab. 17 (1989), no. 2, 586--595. doi:10.1214/aop/1176991417. https://projecteuclid.org/euclid.aop/1176991417