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(2)
Point spectra of some mutually exciting point processes
Spectra of some selfexciting and mutually exciting point processes
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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
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A cluster representation of a self  exciting process
(
Citations: 17
)
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A. G. Hawkes
,
D. Oakes
Published in 1974.
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Citation Context
(7)
...Selfexciting 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 GaltonWatson 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 Stabile
,
et al.
Risk Processes with Nonstationary Hawkes Claims Arrivals
...Very popular and versatile Poisson cluster processes are the socalled selfexciting 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 GaltonWatson process with one ancestor and number of offspring per individual following a Poisson distribution with mean µ (see p. 49
6 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 Bordenave
,
et 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 MØLLER
,
et 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 MØLLER
,
et al.
APPROXIMATE SIMULATION OF HAWKES PROCESSES
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Citations
(17)
Risk Processes with Nonstationary Hawkes Claims Arrivals
(
Citations: 1
)
Gabriele Stabile
,
Giovanni Luca Torrisi
Journal:
Methodology and Computing in Applied Probability  METHODOL COMPUT APPL PROBAB
, vol. 12, no. 3, pp. 415429, 2010
Robust dynamic classes revealed by measuring the response function of a social system
(
Citations: 31
)
Riley Crane
,
Didier Sornette
Journal:
Proceedings of The National Academy of Sciences  PNAS
, vol. 105, no. 41, pp. 1564915653, 2008
Modeling Financial Contagion Using Mutually Exciting Processes
(
Citations: 2
)
Yacine AïtSahalia
,
Roger J. A. Laeven
Published in 2008.
Large deviations of Poisson cluster processes
(
Citations: 1
)
Charles Bordenave
,
Giovanni Luca Torrisi
Journal:
Stochastic Models  STOCH MODELS
, vol. 23, no. 4, pp. 593625, 2007
The pair correlation function of spatial Hawkes processes
(
Citations: 1
)
Jesper Møller
,
Giovanni Luca Torrisi
Journal:
Statistics & Probability Letters  STAT PROBAB LETT
, vol. 77, no. 10, pp. 9951003, 2007