A Poisson process is a process satisfying the following properties:

1. The numbers of changes in nonoverlapping intervals are independent for all intervals.

2. The probability of exactly one change in a sufficiently small interval
is ,
where
is the probability of one change and is the number of trials.

3. The probability of two or more changes in a sufficiently small interval is essentially 0.

In the limit of the number of trials becoming large, the resulting distribution is
called a Poisson distribution.

## See also

Point Process,

Poisson
Distribution
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## References

Grimmett, G. and Stirzaker, D. *Probability and Random Processes, 2nd ed.* Oxford, England: Oxford University Press, 1992.Papoulis,
A. *Probability,
Random Variables, and Stochastic Processes, 2nd ed.* New York: McGraw-Hill,
pp. 548-549, 1984.Ross, S. M. *Stochastic
Processes, 2nd ed.* New York: Wiley, p. 59, 1996.## Referenced
on Wolfram|Alpha

Poisson Process
## Cite this as:

Weisstein, Eric W. "Poisson Process."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/PoissonProcess.html

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