Stationarity and ergodicity of univariate generalized autoregressive score processes

Stationarity of Generalized Autoregressive Moving Average Models

Time series models are often constructed by combining nonstationary effects such as trends with stochastic processes that are believed to be stationary. Although stationarity of the underlying process is typically crucial to ensure desirable properties or even validity of statistical estimators, there are numerous time series models for which this stationarity is not yet proven. A major barrier...

Quasi-stationarity and quasi-ergodicity of General Markov Processes

In this paper we give some general, but easy-to-check, conditions guaranteeing the quasistationarity and quasi-ergodicity of Markov processes. We also present several classes of Markov processes satisfying our conditions. AMS 2010 Mathematics Subject Classification: Primary 60F25, 60J25G20; Secondary 60J35, 60J75

Stationarity and Stability of Autoregressive Neural Network Processes

We analyze the asymptotic behavior of autoregressive neural network (AR-NN) processes using techniques from Markov chains and non-linear time series analysis. It is shown that standard AR-NNs without shortcut connections are asymptotically stationary. If linear shortcut connections are allowed, only the shortcut weights determine whether the overall system is stationary, hence standard conditio...

Random Fields: Stationarity, Ergodicity, and Spectral Behavior

Stationarity, ergodicity, and entropy in relativistic systems

Recent molecular dynamics simulations show that a dilute relativistic gas equilibrates to a Jüttner velocity distribution if ensemble velocities are measured simultaneously in the observer frame. The analysis of relativistic Brownian motion processes, on the other hand, implies that stationary one-particle distributions can differ depending on the underlying timeparameterizations. Using molecul...