Continuous-time stochastic process
In
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]
Examples
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
.
See also
- Continuous signal
References
- ISBN 0-8162-6664-6(Chapter 6)
- ^ ISBN 0-19-920613-9(Entry for "continuous process")
- ISBN 9783319003276. Retrieved 20 June 2022.