Journal article

Invariance principles for homogeneous sums: Universality of Gaussian Wiener chaos

Abstract:: 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.

Publication status:: Published

Actions

Email

Email this record

Send the bibliographic details of this record to your email address.

Your Email
Please enter the email address that the record information will be sent to.

-
Your message (optional)
Please add any additional information to be included within the email.
Cite

Cite this record

APA Style

Nourdin, I., Peccati, G., & Reinert, G. (2009). Invariance principles for homogeneous sums: Universality of Gaussian Wiener chaos. Annals of Probability, 38(5), 1947–1985.

MLA Style

Nourdin, I., et al. “Invariance Principles for Homogeneous Sums: Universality of Gaussian Wiener Chaos.” Annals of Probability, vol. 38, no. 5, 2009, pp. 1947–85.

Chicago Style

Nourdin, I, G Peccati, and G Reinert. 2009. “Invariance Principles for Homogeneous Sums: Universality of Gaussian Wiener Chaos.” Annals of Probability 38 (5): 1947–85.
Share
Print

Access Document

Publisher copy:: 10.1214/10-AOP531

Authors

+ Nourdin, I More by this author

Role:: Author

+ Peccati, G More by this author

Role:: Author

+ Reinert, G More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Statistics
Role:: Author

Journal:: Annals of Probability More from this journal
Volume:: 38
Issue:: 5
Pages:: 1947-1985
Publication date:: 2009-04-07
DOI:: 10.1214/10-AOP531
ISSN:: 0091-1798

Language:: English
Keywords:: math.PR
Pubs id:: pubs:97508
UUID:: uuid:7708c1b7-e64a-47fb-aec6-76e44cbeb2e7
Local pid:: pubs:97508
Source identifiers:: 97508
Deposit date:: 2012-12-19

Terms of use

Copyright date:: 2009
Notes:: Published in at http://dx.doi.org/10.1214/10-AOP531 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org)

Licence:: Terms and Conditions of Use for Oxford University Research Archive

Views and Downloads

About views and downloads

If you are the owner of this record, you can report an update to it here: Report update to this record

TO TOP