Abstract
The chapter deals with the basic notions that characterize a random process in a statistical sense.
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Notes
- 1.
As known, cumulative distribution functions are also termed distribution functions.
- 2.
It is known that the product mean of random variables is not influenced by the presentation order of variables on which it operates.
- 3.
Fluctuations around the mean in a process Section \( {\text{X}}({\text{t}}) \) are the quantities \( {\text{z}}_{\text{i}} \left( {\text{t}} \right) = {\text{x}}_{\text{i}} \left( {\text{t}} \right) - {\text{m}}({\text{t}}) \), or the determinations of the R.V. “centred Section \( {\text{Z}}({\text{t}}) \)” of the process \( {\text{Z}}\left( {\text{t}} \right) = {\text{X}}\left( {\text{t}} \right) - {\text{m}}({\text{t}}) \).
- 4.
The constancy of \( {\text{C}}({\text{t}},{\text{t}}^{ '} ) \) for pairs of time t, t′, anyway placed on T, is a specific form of stationarity, namely the autocovariance stationarity. The autocovariance stationarity is a particular form of weak stationarity (see the following Sect. 2.2).
References
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Mauro, R. (2015). Random Process Fundamentals. In: Traffic and Random Processes. Springer, Cham. https://doi.org/10.1007/978-3-319-09324-6_2
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DOI: https://doi.org/10.1007/978-3-319-09324-6_2
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