Strong law of large numbers with concave moments
Anders Karlsson, Nicolas Monod
TL;DR
This paper demonstrates that the ergodic theorem can be applied to establish a strong law of large numbers for any concave moment, extending classical results in probability theory.
Contribution
It introduces a simple application of the ergodic theorem to prove a strong LLN for all concave moments, broadening the scope of existing laws.
Findings
Strong LLN holds for all concave moments.
Ergodic theorem provides a straightforward proof.
Extension of classical probability results.
Abstract
In this note not intended for publication, it is observed that a wellnigh trivial application of the ergodic theorem of Karlsson-Ledrappier yields a strong LLN for arbitrary concave moments.
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Taxonomy
TopicsProbability and Risk Models · Stochastic processes and financial applications