poisson_process

AProb{ 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.