Abstract
The concept of stochastic process (or random process or briefly process) is used if the random variable X depends on time. We write X t) for t ∈ T. Observing a stochastic process X t), one obtains the realization (or trajectory, path, sample function) of this stochastic process denoted by x t) that is already a real (deterministic) function of the argument t. Practical examples of realizations of stochastic processes are meteorological records, electroencephalograms, records of mechanical vibrations, seismograms, time registrations of failures in reliability tests, etc. The role of probability theory and mathematical statistics in the analysis of stochastic processes consists in the calculation of characteristics describing the behaviour of processes as a whole, in the construction of models that enable us to generate the corresponding processes, in filtering, in prediction, etc.
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© 1994 Springer Science+Business Media New York
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Cipra, T. (1994). Stochastic Processes. In: Survey of Applicable Mathematics. Mathematics and Its Applications, vol 280/281. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8308-4_36
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DOI: https://doi.org/10.1007/978-94-015-8308-4_36
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-015-8310-7
Online ISBN: 978-94-015-8308-4
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