Paper Information

Journal:   BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY   2008 , Volume 34 , Number 1; Page(s) 45 To 58.
 
Paper: 

EXPECTED NUMBER OF LOCAL MAXIMA OF SOME GAUSSIAN RANDOM POLYNOMIALS

 
 
Author(s):  REZA KHAH S.*, SHEMEHSAVAR S.
 
* 
 
Abstract: 

Let Qn(x) =Sni=0  Aixi be a random algebraic polynomial where the coefficients A0,A1, · · · form a sequence of centered Gaussian random variables. Moreover, assume that the increments Dj = Aj - Aj−1, j = 0, 1, 2, · · · , with A−1 = 0, are independent. The coefficients can be considered as n consecutive observations of a Brownian motion. We study the asymptotic behaviour of the expected number of local maxima of Qn(x) below level u = O(nk), for some k > 0.

 
Keyword(s): NORMAL, (T1, T2)-NORMAL, SIGMA -OBTAIABLE, COUPLE TOPOLOGICAL SPACE, SIGMA -NORMAL, SEMICONTINUOUS, SIGMA -CONTINUOUS, SIGMA -URYSOHN’S LEMMA
 
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