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Random Processes and Dynamical Systems

  • Robert M. Gray
Chapter

Abstract

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.

Keywords

Probability Measure Random Process Probability Space Measurable Space Inverse Image 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  1. 1.Department of Electrical EngineeringStanford UniversityStanfordUSA

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