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Published in:
2022 | OriginalPaper | Chapter
8. Discrete-Time Stochastic Processes
Author : Peter Müller
Published in: Handbook of Dynamics and Probability
Publisher: Springer International Publishing
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Abstract
Here we start to extend the concept of random variables to families of random variables \((f_t)_{t\in T}\) where the index set is either \({T=\,{\textsf {I\!\!\!Z}}}\) (\({\,{\textsf {I\!\!\!N}}}\)) or \({\,{\textsf {I\!\!\!R}}}\) (\({\,{\textsf {I\!\!\!R}}_+}\)). The first case represents discrete-time stochastic processes, the second case represents continuous-time stochastic processes. We thus progress up through the general classification of families of random variables.