Discrete-Time Stochastic Process

Context:
- It can range from being a Discrete-Time Discrete-Outcome Stochastic Process to being a Discrete-Time Continuous-Outcome Stochastic Process.
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Example(s):
- a Binomial Stochastic Process.
- a Random Walk Process.
- a Moran Process.
- a Branching Process.
- a Chinese Restaurant Process.
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Counter-Example(s):
- a Continuous-Time Stochastic Process.
- a Discrete-Time Deterministic Process.
See: Discrete State Variable, IID Random Variables.

Referemces

(Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/discrete-time_stochastic_process Retrieved:2015-6-20.
- In probability theory and statistics, a discrete-time stochastic process is a stochastic process for which the index variable takes a discrete set of values, as contrasted with a continuous-time process for which the index variable takes values in a continuous range. An alternative terminology uses discrete parameter as being more inclusive. ^[1] A more restricted class of processes are those with discrete time and discrete state space. The apparently simpler terms "discrete process" or "discontinuous process" may cause confusion with processes having continuous time and discrete state space.^[2] Given the possible confusion, caution is needed.

↑ Parzen, E. (1962) Stochastic Processes, Holden-Day. ISBN 0-8162-6664-6 (page 7)
↑ Dodge, Y. (2006) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9 (Entry for "continuous process")

(Riddles, 2010) ⇒ John Riddles. (2010). “Introduction to Stochastic Processes." Unpublished Glossary. Department of Statistics, Iowa State University.
- QUOTE: Discrete-Time Stochastic Process: A stochastic process indexed by a countable number of time points.