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# Poisson Process

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.

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.

Poisson Process

## Cite this as:

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