Section outline

  • Lecture 13 (08.04.26) -  Homogeneous Poisson process: equivalent definitions, properties, arrival and inter-arrival times. Superposition and decomposition  of Poisson processes. Inhomogeneous Poisson process. Compound  Poisson process: definition and main statistics (average, variance, Laplace trasform).
    Lecture 14 (09.04.26) - Poisson Point processes and (counting) random measures: definition, intensity measure, Laplace functional. Random measure and Laplace functionals. Characterization of Poisson Point processes by Laplace functionals: properties and examples.