Poisson process
A counting process is called a simple Poisson, or simply a Poisson process with parameter , also known as the intensity, if
-
1.
,
- 2.
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3.
,
-
4.
,
where is the O notation.
Remarks.
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•
The intensity is assumed to be a constant in terms of .
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•
Condition 3 above says that the rate in which the an event occurs once in time interval , as approaches 0, is . Condition 4 says that the event occurs more than once is very unlikely (the rate approaches zero as the time interval shrinks to zero).
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It can be shown that has a Poisson distribution (hence the name of the stochastic process) with parameter :
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•
Therefore, .
Title | Poisson process |
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Canonical name | PoissonProcess |
Date of creation | 2013-03-22 15:01:29 |
Last modified on | 2013-03-22 15:01:29 |
Owner | CWoo (3771) |
Last modified by | CWoo (3771) |
Numerical id | 8 |
Author | CWoo (3771) |
Entry type | Definition |
Classification | msc 60G51 |
Synonym | homogeneous Poisson process |
Defines | simple Poisson process |
Defines | intensity |