Martingales with sufficient statistics |
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| Authors: | R Bórquez |
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| Institution: | Department of Agricultural Economics, Pontificia Universidad Católica de Chile, Santiago, Chile. |
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| 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. |
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| Keywords: | Sufficient statistics convex sets of martingale laws dominated martingale Laws convergence of martingales |
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