1 citations · 2 across the 8 of their papers we have counts for
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Markov approximation for controlled Hawkes Jump-Diffusions with general kernels
Mahmoud Khabou, Mehdi Talbi
We present a Markov approximation for jump-diffusions whose jump part consists in a Hawkes process with intensity driven by a general (possibly non-monotone) kernel. Under minimal…
Gaussian Approximation and Moderate Deviations of Poisson Shot Noises with Application to Compound Generalized Hawkes Processes
Mahmoud Khabou, Giovanni Luca Torrisi
In this article, we give explicit bounds on the Wasserstein and the Kolmogorov distances between random variables lying in the first chaos of the Poisson space and the standard Nor…
Functional approximation of the marked Hawkes risk process
Laure Coutin, Mahmoud Khabou
The marked Hawkes risk process is a compound point process for which the occurrence and amplitude of past events impact the future. Thanks to its autoregressive properties, it foun…
Normal approximation of compound Hawkes functionals
Mahmoud Khabou, Nicolas Privault, Anthony Reveillac
We derive quantitative bounds in the Wasserstein distance for the approximation of stochastic integrals with respect to Hawkes processes by a normally distributed random variable.…
Malliavin-Stein method for the multivariate compound Hawkes process
Mahmoud Khabou
In this paper, we provide upper bounds on the d2 distance between a large class of functionals of a multivariate compound Hawkes process and a given Gaussian vector. This is proven…
Convergence of the Discrete-Time Compound Hawkes Processwith Exponential or Erlang Kernel
Lorick Huang, Mahmoud Khabou
Due to its clustering and self-exciting properties, the Hawkes process has been used extensively in numerous fields ranging from sismology to finance. Since data is often aquired o…
The Malliavin-Stein method for Hawkes functionals
Caroline Hillairet, Lorick Huang, Mahmoud Khabou +1
In this paper, following Nourdin-Peccati's methodology, we combine the Malliavin calculus and Stein's method to provide general bounds on the Wasserstein distance between functiona…