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The extended Ville's inequality for nonintegrable nonnegative supermartingales
April 17, 2024, 4:45 a.m. | Hongjian Wang, Aaditya Ramdas
stat.ML updates on arXiv.org arxiv.org
Abstract: Following the initial work by Robbins, we rigorously present an extended theory of nonnegative supermartingales, requiring neither integrability nor finiteness. In particular, we derive a key maximal inequality foreshadowed by Robbins, which we call the extended Ville's inequality, that strengthens the classical Ville's inequality (for integrable nonnegative supermartingales), and also applies to our nonintegrable setting. We derive an extension of the method of mixtures, which applies to $\sigma$-finite mixtures of our extended nonnegative supermartingales. We …
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