Large Deviations for Quadratic Functionals of Gaussian Processes

Włodzimierz Bryc () and Amir Dembo ()

Journal of Theoretical Probability, 1997, vol. 10, issue 2, 307-332

Abstract: Abstract The Large Deviation Principle (LDP) is derived for several quadratic additive functionals of centered stationary Gaussian processes. For example, the rate function corresponding to $$1/T\int {_0^T } X_t^2 dt$$ is the Fenchel-Legendre transform of $$L(y) = - (1/4\pi )\int {_{ - \infty }^\infty } \log (1 - 4\pi yf(s))ds$$ where X t is a continuous time process with the bounded spectral density f(s). This spectral density condition is strictly weaker than the one necessary for the LDP to hold for all bounded continuous functionals. Similar results are obtained for the energy of multivariate discrete-time Gaussian processes and in the regime of moderate deviations, the latter yielding the corresponding Central Limit Theorems.

Keywords: Large deviations; moderate deviations; quadratic additive functionals; Gaussian processes (search for similar items in EconPapers)
Date: 1997
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1023/A:1022656331883 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:10:y:1997:i:2:d:10.1023_a:1022656331883

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1023/A:1022656331883

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().