4 papers
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…
The Markov approximation of the periodic multivariate Poisson autoregression
Mahmoud Khabou, Edward A. K. Cohen, Almut E. D. Veraart
This paper introduces a periodic multivariate Poisson autoregression with potentially infinite memory, with a special focus on the network setting. Using contraction techniques, we…
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…