The Annals of Probability

Stopping Times and Tightness. II

David Aldous

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Abstract

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.

Article information

Source
Ann. Probab., Volume 17, Number 2 (1989), 586-595.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991417

Digital Object Identifier
doi:10.1214/aop/1176991417

Mathematical Reviews number (MathSciNet)
MR985380

Zentralblatt MATH identifier
0686.60036

JSTOR
links.jstor.org

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 60G44: Martingales with continuous parameter

Keywords
Weak convergence tightness martingale

Citation

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


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