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The Malliavin-Stein method for Hawkes functionals.
- Source :
-
ALEA. Latin American Journal of Probability & Mathematical Statistics . 2022, Vol. 19 Issue 2, p1293-1328. 36p. - Publication Year :
- 2022
-
Abstract
- 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 the law of functionals of a compound Hawkes process and the one of a Gaussian random variable. To achieve this, we rely on the Poisson imbedding representation of a Hawkes process to provide a Malliavin calculus for the Hawkes processes, and more generally for compound Hawkes processes. As an application, we close a gap in the literature by providing a quantitative Central Limit Theorem for the compound Hawkes process. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 19800436
- Volume :
- 19
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- ALEA. Latin American Journal of Probability & Mathematical Statistics
- Publication Type :
- Academic Journal
- Accession number :
- 174332336
- Full Text :
- https://doi.org/10.30757/ALEA.v19-52