Poisson Process
Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu · Birkhäuser Boston eBooks · 2010
Consider a certain event that occurs consecutively at random time points $$0 0, i.e., $$N(t) =\sup \{ n :\ {T}_{n} \leq t\},\ \ \mathrm{for}\ \ t > 0.$$ We call N(t),t≥0 a counting process. For each t>0, N(t) could represent the number of accidents at a particular intersection, the number of times a computer breaks down, or similar counts.