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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 process for which the index variable takes only distinct values. An alternative terminology uses **continuous parameter** as being more inclusive.^{[1]}

A more restricted class of processes are the continuous stochastic processes; here the term often (but not always^{[2]}) implies both that the index variable is continuous and that sample paths of the process are continuous. Given the possible confusion, caution is needed.^{[2]}

Continuous-time stochastic processes that are constructed from discrete-time processes via a waiting time distribution are called continuous-time random walks.^{[3]}

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

**^**Parzen, E. (1962)*Stochastic Processes*, Holden-Day. ISBN 0-8162-6664-6 (Chapter 6)- ^
^{a}^{b}Dodge, Y. (2006)*The Oxford Dictionary of Statistical Terms*, OUP. ISBN 0-19-920613-9 (Entry for "continuous process") **^**Paul, Wolfgang; Baschnagel, Jörg (2013-07-11).*Stochastic Processes: From Physics to Finance*. Springer Science & Business Media. pp. 72–74. ISBN 9783319003276. Retrieved 20 June 2022.