Normal Approximation of Compound Hawkes Functionals

• Published in: Journal of theoretical probability Vol. 37; no. 1; pp. 549 - 581
• Main Authors: Khabou, Mahmoud, Privault, Nicolas, Réveillac, Anthony
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2024; Springer Nature B.V; Springer
• Subjects: Approximation; Convergence; Estimates; Mathematical analysis; Mathematics; Mathematics and Statistics; Probability Theory and Stochastic Processes; Random variables; Statistics; Normal approximation; 60G57; Stein’s method; 60G55; 60H07; Malliavin calculus; Hawkes processes; 60F05; normal approximation; Stein method; Malliavin calculus Mathematics Subject Classification : 60G55; Hawkes processes Stein method normal approximation Malliavin calculus Mathematics Subject Classification : 60G55

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. In the case of deterministic and nonnegative integrands, our estimates involve only the third moment of the integrand in...