Continuous-Time Stochastic Process
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A Continuous-Time Stochastic Process is a stochastic process that is a continuous process.
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- Example(s):
- Counter-Example(s):
- See: Stochastic Process, Continuous-Time Process.
Referemces
2012
- http://en.wikipedia.org/wiki/Continuous-time_stochastic_process
- 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.
- 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]
2010
- (Riddles, 2010) ⇒ John Riddles. (2010). “Introduction to Stochastic Processes." Unpublished Glossary. Department of Statistics, Iowa State University.
- QUOTE: Stochastic Process: A Random Variable indexed by time (for an infinite number of time points). Equivalently, it is a Random Vector of infinite dimension.
State Space: X(t) has a support for each value of t. The state space is the union of all of these supports.
- QUOTE: Stochastic Process: A Random Variable indexed by time (for an infinite number of time points). Equivalently, it is a Random Vector of infinite dimension.