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Random Functions

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Stochastic Systems

Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY))

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Abstract

General 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.

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Authors and Affiliations

  1. Cornell University, Hollister Hall, 14853, Ithaca, NY, USA

    Mircea Grigoriu

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  1. Mircea Grigoriu
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Correspondence to Mircea Grigoriu .

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© 2012 Springer-Verlag London Limited

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Grigoriu, M. (2012). Random Functions. In: Stochastic Systems. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-2327-9_3

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  • DOI: https://doi.org/10.1007/978-1-4471-2327-9_3

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-2326-2

  • Online ISBN: 978-1-4471-2327-9

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