Invariance principles for homogeneous sums: Universality of Gaussian Wiener chaos
We compute explicit bounds in the normal and chi-square approximations of multilinear homogenous sums (of arbitrary order) of general centered independent random variables with unit variance. In particular, we show that chaotic random variables enjoy the following form of universality: (a) the norma...
| मुख्य लेखकों: | , , |
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| स्वरूप: | Journal article |
| भाषा: | English |
| प्रकाशित: |
2009
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| _version_ | 1826279810366701568 |
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| author | Nourdin, I Peccati, G Reinert, G |
| author_facet | Nourdin, I Peccati, G Reinert, G |
| author_sort | Nourdin, I |
| collection | OXFORD |
| description | We compute explicit bounds in the normal and chi-square approximations of multilinear homogenous sums (of arbitrary order) of general centered independent random variables with unit variance. In particular, we show that chaotic random variables enjoy the following form of universality: (a) the normal and chi-square approximations of any homogenous sum can be completely characterized and assessed by first switching to its Wiener chaos counterpart, and (b) the simple upper bounds and convergence criteria available on the Wiener chaos extend almost verbatim to the class of homogeneous sums. |
| first_indexed | 2024-03-07T00:04:21Z |
| format | Journal article |
| id | oxford-uuid:7708c1b7-e64a-47fb-aec6-76e44cbeb2e7 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:04:21Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:7708c1b7-e64a-47fb-aec6-76e44cbeb2e72022-03-26T20:20:37ZInvariance principles for homogeneous sums: Universality of Gaussian Wiener chaosJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7708c1b7-e64a-47fb-aec6-76e44cbeb2e7EnglishSymplectic Elements at Oxford2009Nourdin, IPeccati, GReinert, GWe compute explicit bounds in the normal and chi-square approximations of multilinear homogenous sums (of arbitrary order) of general centered independent random variables with unit variance. In particular, we show that chaotic random variables enjoy the following form of universality: (a) the normal and chi-square approximations of any homogenous sum can be completely characterized and assessed by first switching to its Wiener chaos counterpart, and (b) the simple upper bounds and convergence criteria available on the Wiener chaos extend almost verbatim to the class of homogeneous sums. |
| spellingShingle | Nourdin, I Peccati, G Reinert, G Invariance principles for homogeneous sums: Universality of Gaussian Wiener chaos |
| title | Invariance principles for homogeneous sums: Universality of Gaussian
Wiener chaos |
| title_full | Invariance principles for homogeneous sums: Universality of Gaussian
Wiener chaos |
| title_fullStr | Invariance principles for homogeneous sums: Universality of Gaussian
Wiener chaos |
| title_full_unstemmed | Invariance principles for homogeneous sums: Universality of Gaussian
Wiener chaos |
| title_short | Invariance principles for homogeneous sums: Universality of Gaussian
Wiener chaos |
| title_sort | invariance principles for homogeneous sums universality of gaussian wiener chaos |
| work_keys_str_mv | AT nourdini invarianceprinciplesforhomogeneoussumsuniversalityofgaussianwienerchaos AT peccatig invarianceprinciplesforhomogeneoussumsuniversalityofgaussianwienerchaos AT reinertg invarianceprinciplesforhomogeneoussumsuniversalityofgaussianwienerchaos |