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.

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.