Time Intervals and Counting in Point Processes

Bernard Picinbono (1)

1 L2S - Laboratoire des signaux et systèmes

Time point processes can be analyzed in two different ways: by the number of points in arbitrary time intervals or by distance between points. This corresponds to two distinct physical devices: counting or timeinterval measurements. We present an explicit calculation,v alid for arbitrary regular processes,of the statistical properties of time intervals such as residual or life time in terms of counting probabilities. For this calculation, we show that these intervals must be considered as random variables defined by conditional distributions.

Mots clés: Index Terms Counting; point processes; time measurements

Domaines: Sciences de l'ingénieur [physics]; Traitement du signal et de l'image [eess.SP]

Bernard Picinbono. Time Intervals and Counting in Point Processes. IEEE Transactions on Information Theory, 2004, 50, pp.1336 - 1340. ⟨hal-01695059⟩