Spectral conditions for local nondeterminism

Simeon M. Berman

Stochastic Processes and their Applications, 1987, vol. 27, 73-84

Abstract: Let X(t) be a real Gaussian process with stationary increments and spectral distribution function F(x). Put [phi](t)=F([infinity]) - F(1/t). Sufficient conditions in terms of F are given for the process to be locally [phi]-nondeterministic. These are formulated for discrete and absolutely continuous functions F. The results in the discrete case are applied to the analysis of the local time of a random Fourier series with i.i.d. coefficients. The class of distributions of the coefficients includes not only the normal distribution but others such as the symmetric stable distribution.

Keywords: local; nondeterminism; local; time; Gaussian; process; stationarity; spectral; distribution; random; Fourier; series (search for similar items in EconPapers)
Date: 1987
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(87)90006-8
Full text for ScienceDirect subscribers only

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:eee:spapps:v:27:y:1987:i::p:73-84

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().