A counting process is a
stochastic process with values that are non-negative, integer, and non-decreasing:
# ''N''(''t'') ≥ 0.
# ''N''(''t'') is an integer.
# If ''s'' ≤ ''t'' then ''N''(''s'') ≤ ''N''(''t'').
If ''s'' < ''t'', then ''N''(''t'') − ''N''(''s'') is the number of events occurred during the interval
(''s'', ''t''
]. Examples of counting processes include
Poisson process
In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one ...
es and
Renewal processes.
Counting processes deal with the number of occurrences of something over time. An example of a counting process is the number of job arrivals to a queue over time.
If a process has the
Markov property
In probability theory and statistics, the term Markov property refers to the memoryless property of a stochastic process. It is named after the Russian mathematician Andrey Markov. The term strong Markov property is similar to the Markov prop ...
, it is said to be a Markov counting process.
References
* Ross, S.M. (1995) ''Stochastic Processes''. Wiley.
* Higgins JJ, Keller-McNulty S (1995) ''Concepts in Probability and Stochastic Modeling''. Wadsworth Publishing Company. {{ISBN, 0-534-23136-5
Stochastic processes