counting process
A stochastic process is called a counting process if, for each outcome in the sample space ,
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1.
for all ,
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3.
is non-decreasing,
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4.
is right continuous (continuous from the right), and
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5.
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 .
Title | counting process |
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Canonical name | CountingProcess |
Date of creation | 2013-03-22 15:01:19 |
Last modified on | 2013-03-22 15:01:19 |
Owner | CWoo (3771) |
Last modified by | CWoo (3771) |
Numerical id | 5 |
Author | CWoo (3771) |
Entry type | Definition |
Classification | msc 60G51 |