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poisson_process

A poisson process is a never decreasing integer-valued stochastic process N defined through the following properties:
Prob{ N jumps once in infinitesimal time interval dt } = Prob{ dN = 1 } = λdt where λ some perhaps time-dependent constant called the "intensity" of the poisson process.
Prob{ N jumps more than once in infinitesimal time interval dt } = Prob{ dN > 1 } = 0.
Prob{ N does not jump in infinitesimal time interval dt } = Prob{ dN = 0 } = 1-λdt.