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The PoissonPoisson process is a fundamental concept in probability theory and stochastic processes, widely used to model the occurrence of random events over time. While the classical PoissonPoisson process operates in continuous time, many real-world phenomena are observed or recorded in discrete time intervals. This chapter focuses on the discrete-time PoissonPoisson process, an adaptation of the PoissonPoisson process for discrete-time settings. We will explore its definition, properties, and applications, particularly with illustrative numerical examples.

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Poisson  Processes

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  • 发表日期：

    2026年

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  • Muammer Catak,
  • Tofigh Allahviranloo

摘要

The PoissonPoisson process is a fundamental concept in probability theory and stochastic processes, widely used to model the occurrence of random events over time. While the classical PoissonPoisson process operates in continuous time, many real-world phenomena are observed or recorded in discrete time intervals. This chapter focuses on the discrete-time PoissonPoisson process, an adaptation of the PoissonPoisson process for discrete-time settings. We will explore its definition, properties, and applications, particularly with illustrative numerical examples.