Covariance function and ergodicity of asymptotically stationary random fields

Non-stationary Covariance Function

Analyzing datasets, such as sea-level records, pose a challenging statistical problem for reasons including non-stationarity, non-uniformly smooth spatial boundaries, and sparsity in the data. In this paper, we propose a framework to estimate the non-stationary covariance function by employing intrinsic statistics on the local covariates. These local covariates represent the underlying local co...

Random Fields: Stationarity, Ergodicity, and Spectral Behavior

Ergodicity and Gaussianity for Spherical Random Fields

We investigate the relationship between ergodicity and asymptotic Gaussianity of isotropic spherical random fields, in the high-resolution (or high-frequency) limit. In particular, our results suggest that under a wide variety of circumstances the two conditions are equivalent, i.e. the sample angular power spectrum may converge to the population value if and only if the underlying field is asy...

Radiative gravitational fields and asymptotically static or stationary initial data

We describe our present understanding of the relation between the behaviour near space-like infinity of asymptotically flat Cauchy data for Einstein’s vacuum field equations and the asymptotic behaviour of their time evolution at null infinity. It is shown that asymptotically flat, static vacuum solutions admit an analytic conformal representation in a neighbourhood of the critical sets at whic...

The ergodic decomposition of asymptotically mean stationary random sources

It is demonstrated how to represent asymptotically mean stationary (AMS) random sources with values in standard spaces as mixtures of ergodic AMS sources. This an extension of the well known decomposition of stationary sources which has facilitated the generalization of prominent source coding theorems to arbitrary, not necessarily ergodic, stationary sources. Asymptotic mean stationarity gener...