Random Processes and Dynamical Systems
The theoretical fundamentals random variables, random processes, and dynamical systems are developed and elaborated. The emphasis is on discrete time, where the general notion of a dynamical system — a probability space along with a transformation — yields a random process when combined with a random variable. The transformation might, but need not, correspond to a time shift operation. Continuous time processes are discussed briefly by considering a family of ansformations or flow. Probability distributions describing the variables and processes are related using product σ-fields. The basic ideas of codes, filters, factors, and isomorphism are introduced.
KeywordsProbability Measure Random Process Probability Space Measurable Space Inverse Image
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