Real Zeros of a Class of Hyperbolic Polynomials with Random Coefficients

Mina Ketan Mahanti, Amandeep Singh and Lokanath Sahoo

International Journal of Mathematics and Mathematical Sciences, 2015, vol. 2015, 1-7

Abstract:

We have proved here that the expected number of real zeros of a random hyperbolic polynomial of the form , where is a sequence of standard Gaussian random variables, is . It is shown that the asymptotic value of expected number of times the polynomial crosses the level is also as long as does not exceed , where . The number of oscillations of about will be less than asymptotically only if , where or . In the former case the number of oscillations continues to be a fraction of and decreases with the increase in value of . In the latter case, the number of oscillations reduces to and almost no trace of the curve is expected to be present above the level if log .

Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2015/261370.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2015/261370.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:261370

DOI: 10.1155/2015/261370

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 ().