A system of Volterra-like integral equations characterizes the multi-temporal Laplace transform and two-time covariance of non-stationary multivariate Hawkes processes.
Explicit correlations for the Hawkes processes
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In this paper we fill a gap in the literature by providing exact and explicit expressions for the correlation of general Hawkes processes together with its intensity process. Our methodology relies on the Poisson imbedding representation and on recent findings on Malliavin calculus and pseudo-chaotic representation for counting processes.
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Functional Laplace Transform of a Multivariate Hawkes Process, Subsequent Characteristics, and Numerical Approximations
A system of Volterra-like integral equations characterizes the multi-temporal Laplace transform and two-time covariance of non-stationary multivariate Hawkes processes.