Coin-betting is optimal among e-variable frameworks for mean testing of bounded variables, yielding an explicit characterization of all admissible e-variables and e-processes.
Capacities, Measurable Selection and Dynamic Programming Part I: Abstract Framework
2 Pith papers cite this work. Polarity classification is still indexing.
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We give a brief presentation of the capacity theory and show how it derives naturally a measurable selection theorem following the approach of Dellacherie (1972). Then we present the classical method to prove the dynamic programming of discrete time stochastic control problem, using measurable selection arguments. At last, we propose a continuous time extension, that is an abstract framework for the continuous time dynamic programming principle (DPP).
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The paper proves existence of relaxed equilibria for non-exchangeable mean field games with moderate interactions and common noise, and shows asymptotic equivalence between finite-player approximate Nash equilibria and the mean field limit.
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On the optimality of coin-betting for mean estimation
Coin-betting is optimal among e-variable frameworks for mean testing of bounded variables, yielding an explicit characterization of all admissible e-variables and e-processes.