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counting process
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(Definition)
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A stochastic process
 is called a counting process if, for each outcome  in the sample space  ,
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 for all  ,
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 is piecewise constant,
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 is non-decreasing,
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 is right continuous (continuous from the right), and
- for any
 , there is an
 such that  and
 .
Remark. For any  , the random variable  is usually called the number of occurrences of some event by time  . Then, for  ,  is the number of occurrences in the half-open interval ![$ (s,t]$](http://images.planetmath.org:8080/cache/objects/6730/l2h/img18.png "$ (s,t]$") .
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"counting process" is owned by CWoo.
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(view preamble)
Cross-references: half-open interval, event, occurrences, number, random variable, continuous from the right, continuous, right, piecewise, outcome, stochastic process
There are 2 references to this entry.
This is version 2 of counting process, born on 2005-02-09, modified 2005-02-15.
Object id is 6730, canonical name is CountingProcess.
Accessed 3087 times total.
Classification:
| AMS MSC: | 60G51 (Probability theory and stochastic processes :: Stochastic processes :: Processes with independent increments) |
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Pending Errata and Addenda
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