Continuous-time stochastic process: Difference between revisions

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In [[probability theory]] and [[statistics]], a '''continuous-time stochastic process''', or a '''continuous-space-time stochastic process''' is a [[stochastic process]] for which the index variable takes a continuous set of values, as contrasted with a [[discrete-time signal|discrete-time process]] for which the index variable takes only distict values. A more restricted class of processes are the [[continuous stochastic process]]es: here the term often (but not always<ref name=D>Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', OUP. ISBN 0-19-920613-9 (Entry for "continuous process")</ref>) implies both that the index variable is continuous and that sample paths of the process are continuous. Given the possible confusion, caution is needed.<ref name=D/>

#REDIRECT[[continuous stochastic process]]

==Examples==

An example of a continuous-time stochastic process for which sample paths are not continous is a [[Poisson process]]. An example with continuous paths is the [[Ornstein–Uhlenbeck process]].

==References==

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[[Category:Stochastic processes]]

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