Cumulants on Wiener chaos: moderate deviations and the fourth moment theorem

Schulte, Matthias; Thäle, Christoph (2016). Cumulants on Wiener chaos: moderate deviations and the fourth moment theorem. Journal of functional analysis, 270(6), pp. 2223-2248. Elsevier 10.1016/j.jfa.2016.01.002

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A moderate deviation principle as well as moderate and large deviation inequalities for a sequence of elements living inside a fixed Wiener chaos associated with an isonormal Gaussian process are shown. The conditions under which the results are derived coincide with those of the celebrated fourth moment theorem of Nualart and Peccati. The proofs rely on sharp estimates for cumulants. As applications, explosive integrals of a Brownian sheet, a discretized version of the quadratic variation of a fractional Brownian motion and the sample bispectrum of a spherical Gaussian random field are considered.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Schulte, Matthias

Subjects:

500 Science > 510 Mathematics

ISSN:

0022-1236

Publisher:

Elsevier

Language:

English

Submitter:

David Ginsbourger

Date Deposited:

25 Apr 2017 11:17

Last Modified:

25 Apr 2017 11:17

Publisher DOI:

10.1016/j.jfa.2016.01.002

BORIS DOI:

10.7892/boris.93227

URI:

https://boris.unibe.ch/id/eprint/93227

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