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Continuous-time stochastic process

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Through Statistics and Stochastic process

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

Continuous-time stochastic processes that are constructed from discrete-time processes via a waiting time distribution are called continuous-time random walks.

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.

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