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math.DS2025
The pointwise ergodic theorem on finitely additive spaces
Morenikeji Neri
The almost sure convergence of ergodic averages in Birkhoff's pointwise ergodic theorem is known to fail in the finitely additive setting. We introduce a natural reformulation of a…
math.OC2025
An abstract effective convergence theorem for stochastic processes, with applications to stochastic approximation
Morenikeji Neri, Nicholas Pischke, Thomas Powell
We provide a general theorem on the asymptotic behavior of stochastic processes that conform to a relaxed supermartingale condition. The distinguishing feature of our result is tha…