Poisson Process

Sivaprasad Madhira and Shailaja Deshmukh ()
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Sivaprasad Madhira: Savitribai Phule Pune University
Shailaja Deshmukh: Savitribai Phule Pune University

Chapter Chapter 7 in Introduction to Stochastic Processes Using R, 2023, pp 389-440 from Springer

Abstract: Abstract The Poisson process is simple yet the most widely used continuous time Markov chain. It serves as a model for time epochs at which specific events, such as arrivals into a system, occur. In Sect. 2, the Poisson process is defined as a process with stationary and independent increments and it is established that the sojourn times are independent and identically distributed, each having exponential distribution. In Sect. 3, the Poisson process is defined as a point process in which inter-occurrence times are independent and identically distributed, each having exponential distribution. Equivalence of the two definitions is established. Non-homogeneous Poisson processes are studied in Sect. 4. Superposition and decomposition (thinning) of Poisson processes are discussed in Sect. 5. Section 6 deals with compound Poisson processes. The R codes used for numerical examples in the chapter are given in Sect. 7.

Date: 2023
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DOI: 10.1007/978-981-99-5601-2_7

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