Corpus ID: 10766240

# PROBABILITY AND MEASURE

@inproceedings{Norris2013PROBABILITYAM,
title={PROBABILITY AND MEASURE},
author={J. Norris},
year={2013}
}
1,932 Citations
A q-binomial extension of the CRR asset pricing model
• Economics, Mathematics
• 2021
We propose an extension of the Cox-Ross-Rubinstein (CRR) model based on q-binomial (or Kemp) random walks, with application to default with logistic failure rates. This model allows us to considerExpand
L ARGE-WIDTH FUNCTIONAL ASYMPTOTICS FOR DEEP G AUSSIAN NEURAL NETWORKS
In this paper, we consider fully-connected feed-forward deep neural networks where weights and biases are independent and identically distributed according to Gaussian distributions. ExtendingExpand
Large-width functional asymptotics for deep Gaussian neural networks
• Computer Science, Mathematics
• ICLR
• 2021
These results contribute to recent theoretical studies on the interplay between infinitely-wide deep neural networks and Gaussian Processes by establishing weak convergence in function-space with respect to a stronger metric. Expand
Spectral statistics of high dimensional sample covariance matrix with unbounded population spectral norm
In this paper, we establish some new central limit theorems for certain spectral statistics of a high-dimensional sample covariance matrix under a divergent spectral norm population model. This modelExpand
A modern approach to the moment problem on $\mathbb{R}$
• Mathematics
• 2020
The moment problem is an important problem in Functional Analysis and in Probability measure. It goes back to Stieltjes, around 1890. There is still an important ongoing interest in the recentExpand
Analytical Evaluation of Non-Elementary Integrals Involving Some Exponential, Hyperbolic and Trigonometric Elementary Functions and Derivation of New Probability Measures Generalizing the Gamma-Type and Gaussian-Type Distributions
The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, \$ \int x^\alpha e^{\eta x^\beta}dx, \int x^\alpha \cosh\left(\eta x^\beta\right)dx, \intExpand
Equilibrium Existence in Games with Ties
• 2020
We provide conditions that operationalize Reny’s (1999) better-reply security for Bayesian games and use these conditions to prove the existence of equilibria for classes of games in which payoffExpand
Exact posterior distributions of wide Bayesian neural networks
• Computer Science, Mathematics
• ArXiv
• 2020
This work provides the missing theoretical proof that the exact BNN posterior converges (weakly) to the one induced by the GP limit of the prior and shows how to generate exact samples from a finite BNN on a small dataset via rejection sampling. Expand
Infinite attention: NNGP and NTK for deep attention networks
• Computer Science, Mathematics
• ICML
• 2020
A rigorous extension of results to NNs involving attention layers is provided, showing that unlike single- head attention, which induces non-Gaussian behaviour, multi-head attention architectures behave as GPs as the number of heads tends to infinity. Expand
Robust Screens for Non-Competitive Bidding in Procurement Auctions
We document a novel bidding pattern observed in procurement auctions from Japan: winning bids tend to be isolated, and there is a missing mass of close losing bids. This pattern is suspicious in theExpand