Third Cumulant Stein Approximation for Poisson Stochastic Integrals

Nicolas Privault

Journal of Theoretical Probability, 2019, vol. 32, issue 3, 1461-1481

Abstract: Abstract We derive Edgeworth-type expansions for Poisson stochastic integrals, based on cumulant operators defined by the Malliavin calculus. As a consequence we obtain Stein approximation bounds for stochastic integrals, which are based on third cumulants instead of the $$L^3$$ L 3 -norm term found in the literature. The use of the third cumulant results in a convergence rate faster than the classical Berry–Esseen rate for certain examples.

Keywords: Stein approximation; Malliavin calculus; Poisson stochastic integral; Cumulants; Edgeworth expansions; 60H07; 62E17; 60H05 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-018-0817-1

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