The standard H2 optimal filtering problem considers the estimation of a certain output based on the measured output when the input is a zero mean white noise stochastic process of known intensity. In this paper, the inputs are considered to be of two types. The first type of input, as in standard H2 optimal filtering, is a zero mean wide sense stationary white noise, while the second type is a ...

We study estimation of the tail decay parameter of the marginal distribution corresponding to a discrete time, real valued stationary stochastic process. Assuming that the underlying process is short-range dependent, we investigate properties of estimators of the tail decay parameter which are based on the maximal extreme value of the process observed over a sampled time interval. These estimat...

We discuss a formal mathematical framework for certain coupling constructions via minorisation conditions, which are often used to prove bounds on convergence to stationarity of stochastic processes and MCMC algorithms.

In a previous paper, Smith and Weissman have considered estimators of the extremal index of a stationary stochastic process, and have shown that the theoretical properties of these estimators depend on an approximation formula for the extremal index. However, the derivation of this formula was entirely heuristic except for one very special case. In this paper, it is argued that the formula is v...

We explain why aliasing can be detected in a generic temporallysampled stationary signal process. We then define a concept of stationarity that makes sense for single waveforms. (This is done without assuming that the waveform is a sample path of some underlying stochastic process.) We show how to use this concept to detect aliasing in sampled waveforms. The constraint that must be satisfied to...

Abstract The Levinson–Durbin recursion is used to construct the coefficients which define the minimum mean square error predictor of a new observation for a discrete time, second-order stationary stochastic process. As the sample size varies, the coefficients determine what is called a Levinson–Durbin sequence. A generalized Levinson– Durbin sequence is also defined, and we note that binomial c...

This note considers the taboo counterpart of stationarity. A general stochastic process in two-sided time is de ned to be taboo-stationary if its global distribution does not change by shifting the origin to an arbitrary time in the future under taboo, that is, conditionally on some taboo-event not having occurred up to the new time-origin. The main result is the following basic structural char...