Probability and Random Processes

Robert M. Gray
Additional contact information
Robert M. Gray: Stanford University, Department of Electrical Engineering

Chapter l in Probability, Random Processes, and Ergodic Properties, 1988, pp 1-31 from Springer

Abstract: Abstract In this chapter we develop basic mathematical models of discrete time random processes. Such processes are also called discrete time stochastic processes, information sources, and time series. Physically a random process is something that produces a succession of symbols called “outputs” in a random or nondeterministic manner. The symbols produced may be real numbers such as produced by voltage measurements from a transducer, binary numbers as in computer data, two-dimensional intensity fields as in a sequence of images, continuous or discontinuous waveforms, and so on. The space containing all of the possible output symbols is called the alphabet of the random process, and a random process is essentially an assignment of a probability measure to events consisting of sets of sequences of symbols from the alphabet. It is useful, however, to treat the notion of time explicitly as a transformation of sequences produced by the random process. Thus in addition to the common random process model we shall also consider modeling random processes by dynamical systems as considered in ergodic theory.

Keywords: Probability Measure; Random Process; Probability Space; Measurable Space; Event Space (search for similar items in EconPapers)
Date: 1988
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4757-2024-2_1

Ordering information: This item can be ordered from
http://www.springer.com/9781475720242

DOI: 10.1007/978-1-4757-2024-2_1

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().