• DOI:10.1214/AOP/1176991417
• Corpus ID: 8651028

Stopping Times and Tightness. II

@article{Aldous1978StoppingTA,
  title={Stopping Times and Tightness. II},
  author={David J. Aldous},
  journal={Annals of Probability},
  year={1978},
  volume={17},
  pages={586-595}
}

• D. Aldous
• Published 1 April 1978
• Mathematics
• Annals of Probability

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. AMS 1980 subject classifications. Primary 60B10, secondary 60G44.