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18 papers · 2 filters
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…
Limit theorems for Hawkes processes including inhibition
Patrick Cattiaux, Laetitia Colombani, Manon Costa
In this paper we consider some non linear Hawkes processes with signed reproduction function (or memory kernel) thus exhibiting both self-excitation and inhibition. We provide a La…
Asymptotic deviation bounds for cumulative processes
Patrick Cattiaux, Laetitia Colombani, Manon Costa
The aim of this paper is to get asymptotic deviation bounds via a Large Deviation Principle (LDP) for cumulative processes also known as compound renewal processes or renewal-rewar…
Fluctuations of the Stieltjes transform of the empirical spectral distribution of selfadjoint polynomials in Wigner and deterministic diagonal matrices
Serban Belinschi, Mireille Capitaine, Sandrine Dallaporta +1
We investigate the fluctuations around the mean of the Stieltjes transform of the empirical spectral distribution of any selfadjoint noncommutative polynomial in a Wigner matrix an…
Diffusive limits of Lipschitz functionals of Poisson measures
Eustache Besançon, Laure Coutin, Laurent Decreusefond +1
Continuous Time Markov Chains, Hawkes processes and many other interesting processes can be described as solution of stochastic differential equations driven by Poisson measures. P…
Efficient approximation of branching random walk Gibbs measures
Fu-Hsuan Ho, Pascal Maillard
Disordered systems such as spin glasses have been used extensively as models for high-dimensional random landscapes and studied from the perspective of optimization algorithms. In…