Abstract
The Poisson process is the simplest process associated with counting random numbers of points. We begin our study of these processes when the space where the points occur is a one-dimensional, semiinfinite, real line. While there is no mathematical reason to do so, we refer to this space as “time” because temporal phenomena seem to predominate in applications. The study of temporal Poisson-processes permits many of the properties of Poisson processes to be exhibited, but Poisson processes on multidimensional spaces are also important in applications. These are developed in Sec. 2.5.
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Snyder, D.L., Miller, M.I. (1991). Poisson Processes. In: Random Point Processes in Time and Space. Springer Texts in Electrical Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3166-0_2
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DOI: https://doi.org/10.1007/978-1-4612-3166-0_2
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