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Poisson Process

In: Introduction to Stochastic Processes Using R

Author

Listed:
  • Sivaprasad Madhira

    (Savitribai Phule Pune University)

  • Shailaja Deshmukh

    (Savitribai Phule Pune University)

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.

Suggested Citation

  • Sivaprasad Madhira & Shailaja Deshmukh, 2023. "Poisson Process," Springer Books, in: Introduction to Stochastic Processes Using R, chapter 0, pages 389-440, Springer.
    • Handle: RePEc:spr:sprchp:978-981-99-5601-2_7
    DOI: 10.1007/978-981-99-5601-2_7
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