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arXiv · 2203.09687

A Mass Transport Proof of the Ergodic Theorem

Calvin Wooyoung Chin
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Abstract

It is known that a gambler repeating a game with positive expected value has a positive probability to never go broke. We use the mass transport method to prove the generalization of this fact where the gains from the bets form a stationary, rather than an i.i.d., sequence. Birkhoff's ergodic theorem follows from this by a standard argument.

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Calvin Wooyoung Chin. 2022-03-18. A Mass Transport Proof of the Ergodic Theorem. https://arxiv.org/abs/2203.09687

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