Applications of Martingale System Theorems

The Erwin Schrr Odinger International Institute for Mathematical Physics Martingale-diierence Random Fields Limit Theorems and Some Applications Martingale-diierence Random Fields. Limit Theorems and Some Applications

Davis-type Theorems for Martingale Difference Sequences

We study Davis-type theorems on the optimal rate of convergence of moderate deviation probabilities. In the case of martingale difference sequences, under the finite pth moments hypothesis (1 ≤ p <∞), and depending on the normalization factor, our results show that Davis’ theorems either hold if and only if p > 2 or fail for all p ≥ 1. This is in sharp contrast with the classical case of i.i.d....

Limit Theorems for Spectra of Random Matrices with Martingale Structure

We study classical ensembles of real symmetric random matrices introduced by Eugene Wigner. We discuss Stein’s method for the asymptotic approximation of expectations of functions of the normalized eigenvalue counting measure of high dimensional matrices. The method is based on a differential equation for the density of the semi-circular law.

Martingale limit theorems revisited and non-linear cointegrating regression

For a certain class of martingales, the convergence to mixture normal distribution is established under the convergence in distribution for the conditional variance. This is less restrictive in comparison with the classical martingale limit theorem where one generally requires the convergence in probability. The extension removes a main barrier in the applications of the classical martingale li...

BSDEs , martingale problems , pseudo - PDEs and applications