Abstract
The first two sections of this chapter demonstrate the power of the martingale approach to point processes by means of simple examples which may serve as an introduction to the more elaborate theory and applications. The last section treats two issues that come up when sampling a wide-sense stationary stochastic process at random times forming a point process: firstly, how much of the original power spectral measure can be recovered from the random samples? and secondly, how far from the original is the process obtained by linear filtering applied to the sampled signal? The classical Shannon–Nyquist reconstruction theorem of bandlimited signals is a particular case of the general theory.
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Brémaud, P. (2020). The Information Content of Point Processes. In: Point Process Calculus in Time and Space. Probability Theory and Stochastic Modelling, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-030-62753-9_10
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DOI: https://doi.org/10.1007/978-3-030-62753-9_10
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