A counting process is a
stochastic process
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ...
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 processes 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, 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