Mean number of real zeros of a random trigonometric polynomial IV

J. Ernest Wilkins

International Journal of Stochastic Analysis, 1997, vol. 10, 1-4

Abstract:

If a j ( j = 1 , 2 , … , n ) are independent, normally distributed random variables with mean 0 and variance 1 , if p is one half of any odd positive integer except one, and if v n p is the mean number of zeros on ( 0 , 2 π ) of the trigonometric polynomial a 1 cos x + 2 p a 2 cos 2 x + … + n p a n cos n x , then v n p = μ p { ( 2 n + 1 ) + D 1 p + ( 2 n + 1 ) − 1 D 2 p + ( 2 n + 1 ) − 2 D 3 p } + O { ( 2 n + 1 ) − 3 } , in which μ p = { ( 2 p + 1 ) / ( 2 p + 3 ) } ½ , and D 1 p , D 2 p and D 3 p are explicitly stated constants.

Date: 1997
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJSA/10/296454.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJSA/10/296454.xml (text/xml)

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:hin:jnijsa:296454

DOI: 10.1155/S1048953397000063

Access Statistics for this article

More articles in International Journal of Stochastic Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().