Third cumulant stein approximation for Poisson stochastic integrals

Third cumulant stein approximation for Poisson stochastic integrals

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....

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Main Author: Privault, Nicolas
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2021
Subjects:
Science::Mathematics
Stein Approximation
Malliavin Calculus
Online Access:https://hdl.handle.net/10356/148588
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1485882023-02-28T19:54:37Z Third cumulant stein approximation for Poisson stochastic integrals Privault, Nicolas School of Physical and Mathematical Sciences Science::Mathematics Stein Approximation Malliavin Calculus 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. Ministry of Education (MOE) Accepted version This research was supported by the Singapore MOE Tier 2 Grant MOE2016-T2-1- 036. 2021-04-30T04:15:33Z 2021-04-30T04:15:33Z 2019 Journal Article 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 0894-9840 0000-0003-4148-8543 https://hdl.handle.net/10356/148588 10.1007/s10959-018-0817-1 2-s2.0-85042355777 3 32 1461 1481 en MOE2016-T2-1- 036. Journal of Theoretical Probability © 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. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics
Stein Approximation
Malliavin Calculus
spellingShingle Science::Mathematics
Stein Approximation
Malliavin Calculus
Privault, Nicolas
Third cumulant stein approximation for Poisson stochastic integrals
description 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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Privault, Nicolas
format Article
author Privault, Nicolas
author_sort Privault, Nicolas
title Third cumulant stein approximation for Poisson stochastic integrals
title_short Third cumulant stein approximation for Poisson stochastic integrals
title_full Third cumulant stein approximation for Poisson stochastic integrals
title_fullStr Third cumulant stein approximation for Poisson stochastic integrals
title_full_unstemmed Third cumulant stein approximation for Poisson stochastic integrals
title_sort third cumulant stein approximation for poisson stochastic integrals
publishDate 2021
url https://hdl.handle.net/10356/148588
_version_ 1759856401673355264

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