11 papers
Logical Metatheorems for Abstract Spaces axiomatized in Positive Bounded Logic II: Metric spaces and the model-theoretic uniformity principle
Ulrich Kohlenbach, Morenikeji Neri, Jin Wei
We extend the proof-theoretic treatment of uniform bound extraction from normed structures axiomatized in positive bounded logic [Advances in Mathematics, 290:503-551, 2016] (as de…
Quantitative limit theorems for generalized Pólya urns with applications to random tree models
Morenikeji Neri, Pedro Pinto
We establish novel quantitative limit theorems for the asymptotic distribution of colours in a generalized Pólya urn. Concretely, we construct explicit rates of convergence for th…
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…
A systematic way of analysing proofs in probability theory
Morenikeji Neri, Paulo Oliva, Nicholas Pischke
Over extended systems of finite type arithmetic, we utilize a formal representation of the outer measure to define a translation which allows for the systematic formalization of pr…
Generalized fluctuation bounds for stochastic algorithms in the presence of compactness
Morenikeji Neri, Nicholas Pischke, Thomas Powell
We provide a convergence result for sequences of random variables taking values in a metric space that satisfy a stochastic quasi-Fejér monotonicity condition, in the context of a…
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…