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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| Format: | Article |
| Language: | English |
| Published: |
2021
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| Online Access: | https://hdl.handle.net/10356/148588 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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. |
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