Extrapolation of Stationary Random Fields

We introduce basic statistical methods for the extrapolation of stationary random fields. For square integrable fields, we set out basics of the kriging extrapolation techniques. For (non--Gaussian) stable fields, which are known to be heavy tailed, we describe further extrapolation methods and discuss their properties. Two of them can be seen as direct generalizations of kriging.Comment: 52 pages, 25 figures. This is a review article, though Section 4 of the article contains new results on the weak consistency of the extrapolation methods as well as new extrapolation methods for $\alpha$-stable fields with $0<\alpha\leq 1

Introduction to Random Signals and Noise

Random signals and noise are present in many engineering systems and networks. Signal processing techniques allow engineers to distinguish between useful signals in audio, video or communication equipment, and interference, which disturbs the desired signal. With a strong mathematical grounding, this text provides a clear introduction to the fundamentals of stochastic processes and their practical applications to random signals and noise. With worked examples, problems, and detailed appendices, Introduction to Random Signals and Noise gives the reader the knowledge to design optimum systems for effectively coping with unwanted signals.\ud \ud Key features:\ud • Considers a wide range of signals and noise, including analogue, discrete-time and bandpass signals in both time and frequency domains.\ud • Analyses the basics of digital signal detection using matched filtering, signal space representation and correlation receiver.\ud • Examines optimal filtering methods and their consequences.\ud • Presents a detailed discussion of the topic of Poisson processed and shot noise.\u

Competing with stationary prediction strategies

In this paper we introduce the class of stationary prediction strategies and construct a prediction algorithm that asymptotically performs as well as the best continuous stationary strategy. We make mild compactness assumptions but no stochastic assumptions about the environment. In particular, no assumption of stationarity is made about the environment, and the stationarity of the considered strategies only means that they do not depend explicitly on time; we argue that it is natural to consider only stationary strategies even for highly non-stationary environments.Comment: 20 page