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Stein approximation for multidimensional Poisson random measures by third cumulant expansions
- Publication Year :
- 2018
-
Abstract
- We obtain Stein approximation bounds for stochastic integrals with respect to a Poisson random measure over ${\Bbb R}^d$, $d\geq 2$. This approach relies on third cumulant Edgeworth-type expansions based on derivation operators defined by the Malliavin calculus for Poisson random measures. The use of third cumulants can exhibit faster convergence rates than the standard Berry-Esseen rate for some sequences of Poisson stochastic integrals.
- Subjects :
- Mathematics - Probability
62E17, 60H07, 60H05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1806.00235
- Document Type :
- Working Paper