Some limit theorems for Hawkes processes and application to financial statistics

By Emmanuel Bacry, Sylvain Delattre, Marc Hoffmann, Jean-François Muzy. 2013

223 citations recorded by the source corpus.

Subfields: Applied Mathematics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/020ff9259dd269fe2163f0fc507ea766bfadb35e

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Citations in the corpus

The characteristic function of rough Heston models (2016, methodology): “2 Wiener-Hopf equations The following result is used extensively in this work to solve Wiener-Hopf type equations, see for example [3].”
Large deviations for Markovian nonlinear Hawkes processes (2011, background): “[1], and it was proved for nonlinear Hawkes processes in Zhu [28].”
HAWKES PROCESSES ON LARGE NETWORKS (2016, unknown): “Point 2 is of course related to the classical law of large numbers for multivariate Hawkes processes; see, for example, Brémaud and Massoulié [9] or [3].”
Renewal in Hawkes processes with self-excitation and inhibition (2018, methodology): “Introduction and main results Hawkes processes were introduced by Hawkes [18] and are now widely used in many applications, including modeling of earthquake occurrences [19], [27], finance [2], [1], [3], genetics [31], and neuroscience [9], [14], [29].”
Hawkes model for price and trades high-frequency dynamics (2013, methodology): “In the large time limit, one can show that these processes converge to correlated Brownian motions (see Bacry et al. (2013a) or section 3.3†).”
Perfect hedging in rough Heston models (2017, methodology): “2 Wiener-Hopf equations The following result enables us to solve Wiener-Hopf type equations, see for example [3] for details.”
Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes (2015, background): “2In fact, for a Hawkes process, the no explosion property can be obtained under weaker conditions, for example ∫ t 0 φ(s) ds < ∞ for any t > 0; see [5].”
Limit Theorems for Marked Hawkes Processes with Application to a Risk Model (2012, background): “Recently, Bacry et al.[1] proved a functional central limit theorem for the linear multivariate Hawkes process under certain assumptions, that include the linear Hawkes process as a special case, and they proved that N·t − ·μt √ t → σB(·), as t → ∞, (1.”
Hawkes Processes in Finance (2015, background): “[4], the authors established that under general conditions, the empirical covariation of a multivariate Hawkes process converges towards its expected value, that can be easily expressed in terms of the Hawkes covariance matrix c(t) as given by Eq.”