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ProcessParameterAssumptions[proc]

gives a logical expression for assumptions on parameters in the random process proc.

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ProcessParameterAssumptions

ProcessParameterAssumptions[proc]

gives a logical expression for assumptions on parameters in the random process proc.

Details

  • ProcessParameterAssumptions returns a logical combination of equalities, inequalities, and domain specifications for assumptions on parameters in proc.
  • ProcessParameterAssumptions can generate parameter assumptions for any random process specified as a symbolic process.

Examples

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Basic Examples  (1)

Find the parameter assumptions for different processes:

Wolfram Language code: ProcessParameterAssumptions[GeometricBrownianMotionProcess[μ, σ, θ]]
Wolfram Language code: ProcessParameterAssumptions[PoissonProcess[λ]]
Wolfram Language code: ProcessParameterAssumptions[RandomWalkProcess[p, q]]

Scope  (2)

Obtain assumptions for parameters used in a process:

Wolfram Language code: ProcessParameterAssumptions[BrownianBridgeProcess[{1, a}, {2, b}]]
Wolfram Language code: ProcessParameterAssumptions[RandomWalkProcess[p, .2]]//Simplify

Parameter assumptions for a queueing process:

Wolfram Language code: ProcessParameterAssumptions[QueueingProcess[λ, μ]]

Discrete Markov chain:

Wolfram Language code: ProcessParameterAssumptions[DiscreteMarkovProcess[1, {{1 / 3, p12}, {p21, 1 / 2}}]]

Time series:

Wolfram Language code: ProcessParameterAssumptions[ARMAProcess[{a}, {b}, σ]]

Properties & Relations  (1)

ProcessParameterAssumptions returns True, False, or conditions on the parameters:

Wolfram Language code: ProcessParameterAssumptions[RandomWalkProcess[1 / 3]]
Wolfram Language code: ProcessParameterAssumptions[RandomWalkProcess[-1]]
Wolfram Language code: ProcessParameterAssumptions[RandomWalkProcess[p]]

Possible Issues  (1)

For a fixed time, a random process behaves like a distribution:

Wolfram Language code: ProcessParameterAssumptions[WienerProcess[μ, σ][t]]

Use DistributionParameterAssumptions:

Wolfram Language code: DistributionParameterAssumptions[WienerProcess[μ, σ][t]]
Wolfram Research (2012), ProcessParameterAssumptions, Wolfram Language function, https://reference.wolfram.com/language/ref/ProcessParameterAssumptions.html.

Text

Wolfram Research (2012), ProcessParameterAssumptions, Wolfram Language function, https://reference.wolfram.com/language/ref/ProcessParameterAssumptions.html.

CMS

Wolfram Language. 2012. "ProcessParameterAssumptions." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ProcessParameterAssumptions.html.

APA

Wolfram Language. (2012). ProcessParameterAssumptions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ProcessParameterAssumptions.html

BibTeX

@misc{reference.wolfram_2026_processparameterassumptions, author="Wolfram Research", title="{ProcessParameterAssumptions}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/ProcessParameterAssumptions.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_processparameterassumptions, organization={Wolfram Research}, title={ProcessParameterAssumptions}, year={2012}, url={https://reference.wolfram.com/language/ref/ProcessParameterAssumptions.html}, note=[Accessed: 12-June-2026]}