Local maxima of a random algebraic polynomial

K. Farahmand and P. Hannigan

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 25, 1-13

Abstract:

We present a useful formula for the expected number of maxima of a normal process ξ ( t ) that occur below a level u . In the derivation we assume chiefly that ξ ( t ) , ξ ′ ( t ) , and ξ ′ ′ ( t ) have, with probability one, continuous 1 dimensional distributions and expected values of zero. The formula referred to above is then used to find the expected number of maxima below the level u for the random algebraic polynomial. This result highlights the very pronounced difference in the behaviour of the random algebraic polynomial on the interval ( − 1 , 1 ) compared with the intervals ( − ∞ , − 1 ) and ( 1 , ∞ ) . It is also shown that the number of maxima below the zero level is no longer O ( log n ) on the intervals ( − ∞ , − 1 ) and ( 1 , ∞ ) .

Date: 2001
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/25/973186.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/25/973186.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:jijmms:973186

DOI: 10.1155/S016117120100391X

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().