On limit theorems for fields of martingale differences

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

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...

Notes on the Martingale Approach to Central Limit Theorems for Markov Chains

Notes on the Maxwell-Woodroofe martingale approach to central limit theorems for Markov chains.

Central Limit Theorems for Non-Linear Functionals of Gaussian Fields

In the present paper it is shown that the central limit theorem holds for some non-linear functionals of stationary Gaussian fields if the correlation function of the underlying field tends fast enough to zero. The results are formulated in terms of the Hermite rank of the functional and of the rate of the correlation function. Then we show an example when the limit field is self-similar and Ga...