Poisson Processes and a Bessel Function Integral
Copyright policy )Poisson Processes and a Bessel Function Integral
The probability of winning a simple game of competing Poisson processes turns out to be equal to the well-known Bessel function integral J(x,y) [cf. \textit{Y. L. Luke}, Integrals of Bessel functions. (1962; Zbl 0106.043)]. Several properties of J, some of which seem to be new, follow quite easily from this probabilistic interpretation. The results are applied to the random telegraph process as considered by \textit{M. Kac} [Rocky Mt. J. Math. 4, 497-509 (1974; Zbl 0314.60052)].
- Technical University Eindhoven Netherlands
random telegraph process, probability of winning a simple game, Point processes (e.g., Poisson, Cox, Hawkes processes), Bessel function, Signal detection and filtering (aspects of stochastic processes)
random telegraph process, probability of winning a simple game, Point processes (e.g., Poisson, Cox, Hawkes processes), Bessel function, Signal detection and filtering (aspects of stochastic processes)
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