Random Functions

Abstract

AbstractGeneral considerations on random functions are followed by essential definitions and properties for these functions. The concepts of weak stationarity and stationarity are defined and illustrated. Mean square continuity, differentiation, and integration as well as spectral and related representations for weakly stationary random functions are discussed extensively. Limitations of second moment calculus are highlighted by the study of sample properties for random functions with finite variance. A broad range of random functions, for example, Gaussian, translation, Markov, martingales, Brownian motion, compound Poisson, and Lévy processes, are examined. Algorithms for generating samples of stationary Gaussian functions, translation models, and non-stationary Gaussian processes conclude our discussion.KeywordsBrownian MotionSpectral DensityCovariance FunctionRandom FunctionTranslation ModelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.