Martingales with sufficient statistics. Issue 2 (17th February 2018)

• Record Type: Journal Article
• Authors: Bórquez, R.
• Is Part Of: Stochastics. Volume 90:Issue 2(2018)
• Page Start: 165
• Page End: 171
• Publication Date: 2018-02-17
• Subjects: Sufficient statistics -- convex sets of martingale laws -- dominated martingale Laws -- convergence of martingales; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2017.1316271
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract: The property of countable convexity of the set which contains all dominated martingale laws, for a family of measurable functions with values in a separable Borel space, is proved to be equivalent to the existence of a sufficient statistic. The result is then used to derive a representation of such laws in terms of their extreme points, which are laws of uniformly integrable martingales. Finally, we show that martingales with sufficient statistics converge with probability 1.