Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/148588
Title: Third cumulant stein approximation for Poisson stochastic integrals
Authors: Privault, Nicolas
Keywords: Science::Mathematics
Issue Date: 2019
Source: Privault, N. (2019). Third cumulant stein approximation for Poisson stochastic integrals. Journal of Theoretical Probability, 32(3), 1461-1481. https://dx.doi.org/10.1007/s10959-018-0817-1
Project: MOE2016-T2-1- 036.
Journal: Journal of Theoretical Probability
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 -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.
URI: https://hdl.handle.net/10356/148588
ISSN: 0894-9840
DOI: 10.1007/s10959-018-0817-1
Rights: © 2018 Springer Science+Business Media. This is a post-peer-review, pre-copyedit version of an article published in Journal of Theoretical Probability. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10959-018-0817-1.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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