2: Poisson Processes
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- 2.1: Introduction to Poisson Processes
- A Poisson process is a simple and widely used stochastic process for modeling the times at which arrivals enter a system. It is in many ways the continuous-time version of the Bernoulli process.
- 2.2: Definition and Properties of a Poisson Process
- A Poisson process is an example of an arrival process, and the interarrival times provide the most convenient description since the interarrival times are defined to be IID.
- 2.6: Summary
- We started the chapter with three equivalent definitions of a Poisson process—first as a renewal process with exponentially distributed inter-renewal intervals, second as a stationary and independent increment counting process with Poisson distributed arrivals in each interval, and third essentially as a limit of shrinking Bernoulli processes.
Thumbnail: A visual depiction of a Poisson point process starting from 0, in which increments occur continuously and independently at rate λ. (CC0; Bilorv via Wikipedia)