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A cluster representation of a self - exciting process

A cluster representation of a self - exciting process,A. G. Hawkes,D. Oakes

A cluster representation of a self - exciting process   (Citations: 17)
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Published in 1974.
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    • ...Self-exciting or Hawkes processes (Hawkes 1971a, b; Hawkes and Oakes 1974;...
    • ...Remark 2.1 The Hawkes process Xe with immigrants following a homogeneous Poisson process with intensity ν> 0 on the whole line and fertility rate h(·) is ergodic with intensity ν/(1 − μ) (see Hawkes and Oakes 1974; see also Brémaud and Massoulié 1996)...
    • ...It remains to prove Eq. 18. Recall that the total number of points in a cluster S is equal to the total progeny of the Galton-Watson process with one ancestor and number of offspring per individual following a Poisson distribution with mean μ (see p.496 of Hawkes and Oakes 1974)...

    Gabriele Stabileet al. Risk Processes with Non-stationary Hawkes Claims Arrivals

    • ...Very popular and versatile Poisson cluster processes are the so-called self-exciting or Hawkes processes (Hawkes (1971a), (1971b); Hawkes and Oakes (1974))...
    • ...Recalling that the total number of points in a cluster is equivalent to the total progeny of the Galton-Watson process with one ancestor and number of offspring per individual following a Poisson distribution with mean µ (see p. 496 of Hawkes and Oakes (1974)), the other condition µ < 1 is equivalent to assuming that E[S] = 1/(1 − µ) < ∞. For our purposes it is important to recall that for Hawkes processes the ...

    Charles Bordenaveet al. Large deviations of Poisson cluster processes

    • ...Classical Hawkes processes [4, 6, 7, 8, 9] and their extensions to marked Hawkes...

    JESPER MØLLER. SECOND ORDER ANALYSIS FOR SPATIAL HAWKES PROCESSES

    • ...Section 4 determines an integral equation for F by generalising a result in Hawkes and Oakes [13]...
    • ...result in [13] about the mean length of a cluster...
    • ...a generalisation of Theorem 5 in Hawkes and Oakes [13], which is proved using void...

    JESPER MØLLERet al. PERFECT SIMULATION OF HAWKES PROCESSES

    • ...This paper concerns a useful simulation algorithm for unmarked and marked Hawkes processes [5, 6, 7, 8, 10]...

    JESPER MØLLERet al. APPROXIMATE SIMULATION OF HAWKES PROCESSES

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