Supermartingales as Radon–Nikodym densities and related measure extensions

Nicolas Perkowski; Johannes Ruf

doi:10.1214/14-AOP956

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November 2015 Supermartingales as Radon–Nikodym densities and related measure extensions

Nicolas Perkowski, Johannes Ruf

Ann. Probab. 43(6): 3133-3176 (November 2015). DOI: 10.1214/14-AOP956

Abstract

Certain countably and finitely additive measures can be associated to a given nonnegative supermartingale. Under weak assumptions on the underlying probability space, existence and (non)uniqueness results for such measures are proven.

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Nicolas Perkowski. Johannes Ruf. "Supermartingales as Radon–Nikodym densities and related measure extensions." Ann. Probab. 43 (6) 3133 - 3176, November 2015. https://doi.org/10.1214/14-AOP956