Stationary random processes associated with point processes, springer

Random Sampling of Random Processes: Stationary Point Processes

This is the first of a series of papers treating randomly sampled random processes. Spectral analysis of the resulting samples presupposes knowledge of the statistics of 1 t~}, the random point process whose variates represent the sampling times. We introduce a class of s ta t ionary point processes, whose s ta t ionar i ty (as characterized by any of several equivalent criteria) leads to wide-...

Random Functions and Point Processes

Memory-Universal Prediction of Stationary Random Processes

We consider the problem of one-step-ahead prediction of a real-valued, stationary, strongly mixing random process fXig1i= 1. The best mean-square predictor of X0 is its conditional mean given the entire infinite past fXig 1 i= 1. Given a sequence of observations X1 X2 XN , we propose estimators for the conditional mean based on sequences of parametric models of increasing memory and of increasi...

The Theory of Stationary Point Processes

A b s t r a c t A n a x i o m a t i c f o r m u l a t i o n is p r e s e n t e d fo r p o i n t p r o c e s s e s w h i c h m a y b e i n t e r p r e t e d as o r d e r e d s e q u e n c e s of p o i n t s r a n d o m l y l o c a t e d o n t h e r e a l l ine . S u c h c o n c e p t s a s f o r w a r d r e c u r r e n c e t i m e s a n d n u m b e r of p o i n t s i n i n t e r v a l s a r e d ...

Spectral decomposition of locally stationary random processes

The notion of a locally stationary process is introduced by Silverman in [ l j . This is a new kind of a random process generalizing the notion of a weakly station­ ary process. Let {x(t)}, teR1bsa random process, generally complex, with vanishing mean value and finite covariance function R(s, t) = E{x(s) x(r)} on Wj x Mu where x(t) is the complex conjugate to x(r). The author of [ l j says tha...