Journal
ADVANCES IN APPLIED PROBABILITY
Volume 34, Issue 1, Pages 205-222Publisher
APPLIED PROBABILITY TRUST
DOI: 10.1017/S0001867800011460
Keywords
point process; shot noise; Hawkes process; Bartlett spectra
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We give (i) the Cramer power spectral measure of the general shot noise process with random excitation and non-Poisson stationary driving point processes and (ii) the Bartlett power spectral measure of the self-exciting Hawkes point process with random excitation, also called the Hawkes branching point process with random fertility rate. The latter is obtained via the isometry formula for integrals with respect to the canonical martingale measure associated with a marked point process.
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