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ProcessParameterAssumptions
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ProcessParameterAssumptions

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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)Summary of the most common use cases

Find the parameter assumptions for different processes:

In[1]:=1
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https://wolfram.com/xid/0ixd76lkxri6sgj-srdarp
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0ixd76lkxri6sgj-82c021
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0ixd76lkxri6sgj-okvzfu
Out[3]=3

Scope  (2)Survey of the scope of standard use cases

Obtain assumptions for parameters used in a process:

In[1]:=1
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https://wolfram.com/xid/0ixd76lkxri6sgj-fx46h0
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0ixd76lkxri6sgj-makshy
Out[2]=2

Parameter assumptions for a queueing process:

In[1]:=1
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https://wolfram.com/xid/0ixd76lkxri6sgj-h77xb2
Out[1]=1

Discrete Markov chain:

In[2]:=2
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https://wolfram.com/xid/0ixd76lkxri6sgj-ekekka
Out[2]=2

Time series:

In[3]:=3
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https://wolfram.com/xid/0ixd76lkxri6sgj-bhh2n6
Out[3]=3

Properties & Relations  (1)Properties of the function, and connections to other functions

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

In[1]:=1
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https://wolfram.com/xid/0ixd76lkxri6sgj-ivw16
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0ixd76lkxri6sgj-cb86zz
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0ixd76lkxri6sgj-esvmro
Out[3]=3

Possible Issues  (1)Common pitfalls and unexpected behavior

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

In[1]:=1
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https://wolfram.com/xid/0ixd76lkxri6sgj-5rlodk
Out[1]=1

Use DistributionParameterAssumptions:

In[2]:=2
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https://wolfram.com/xid/0ixd76lkxri6sgj-m9qd0n
Out[2]=2
Wolfram Research (2012), ProcessParameterAssumptions, Wolfram Language function, https://reference.wolfram.com/language/ref/ProcessParameterAssumptions.html.
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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.

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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.

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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

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

BibTeX

@misc{reference.wolfram_2025_processparameterassumptions, author="Wolfram Research", title="{ProcessParameterAssumptions}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/ProcessParameterAssumptions.html}", note=[Accessed: 19-June-2025 ]}

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@misc{reference.wolfram_2025_processparameterassumptions, author="Wolfram Research", title="{ProcessParameterAssumptions}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/ProcessParameterAssumptions.html}", note=[Accessed: 19-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_processparameterassumptions, organization={Wolfram Research}, title={ProcessParameterAssumptions}, year={2012}, url={https://reference.wolfram.com/language/ref/ProcessParameterAssumptions.html}, note=[Accessed: 19-June-2025 ]}

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@online{reference.wolfram_2025_processparameterassumptions, organization={Wolfram Research}, title={ProcessParameterAssumptions}, year={2012}, url={https://reference.wolfram.com/language/ref/ProcessParameterAssumptions.html}, note=[Accessed: 19-June-2025 ]}