StationaryDistribution[proc]
represents the stationary distribution of the process proc, when it exists.


StationaryDistribution
StationaryDistribution[proc]
represents the stationary distribution of the process proc, when it exists.
Details

- Stationary distribution is also known as limiting distribution, steady-state distribution, and invariant distribution.
- The stationary distribution, if it exists, is a slice distribution that is independent of the time
and characterizes the limiting behavior of the process proc after all possible transients have vanished.
- StationaryDistribution[proc] is equivalent to SliceDistribution[proc,∞].
Examples
open all close allBasic Examples (1)
Scope (3)
Stationary distribution may autoevaluate to known distribution:
Stationary distribution may autoevaluate to a derived distribution:
Compute the stationary distribution for a discrete Markov process:
Visualize the convergence to the stationary distribution using the PDF:
Properties & Relations (3)
Stationary distribution is the SliceDistribution at infinity:
The stationary distribution may depend on the initial state:
Mean system size is the mean of the stationary distribution for a queue:
See Also
Related Guides
History
Text
Wolfram Research (2012), StationaryDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/StationaryDistribution.html.
CMS
Wolfram Language. 2012. "StationaryDistribution." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/StationaryDistribution.html.
APA
Wolfram Language. (2012). StationaryDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/StationaryDistribution.html
BibTeX
@misc{reference.wolfram_2025_stationarydistribution, author="Wolfram Research", title="{StationaryDistribution}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/StationaryDistribution.html}", note=[Accessed: 09-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_stationarydistribution, organization={Wolfram Research}, title={StationaryDistribution}, year={2012}, url={https://reference.wolfram.com/language/ref/StationaryDistribution.html}, note=[Accessed: 09-August-2025]}