First-exit times for Poisson shot noise

First-exit times for Poisson shot noise

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Article ID: iaor20021473
Country: United States
Volume: 17
Issue: 1
Start Page Number: 25
End Page Number: 38
Publication Date: Jan 2001
Journal: Communications in Statistics - Stochastic Models
Authors: , ,
Abstract:

For a shot-noise process X(t) with Poisson arrival times and exponentially diminishing shocks of i.i.d. sizes, we consider the first time Tb at which a given level b > 0 is exceeded. An integral equation for the joint density of Tb and X(Tb) is derived and, for the case of exponential jumps, solved explicitly in terms of Laplace transforms.

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