Counting process

A counting process is a stochastic process \{N(t), t\geq0\} with values that are non-negative, integer, and non-decreasing: # N(t)\geq0. # N(t) is an integer. # If s\leq t then N(s)\leq N(t). If s , 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.

A counting process is a stochastic process \{N(t), t\geq0\} with values that are non-negative, integer, and non-decreasing: N(t)\geq0. N(t) is an integer. If s\leq t then N(s)\leq N(t). If s , 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. ==See also== Intensity of counting processes Poisson point process (example for a 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.

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