Expected Number of Local Maxima of Some Gaussian Random Polynomials

dc.creatorShemehsavar, S.
dc.creatorRezakhah, S.
dc.date2006-05-04
dc.date.accessioned2026-07-07T07:13:54Z
dc.date.available2026-07-07T07:13:54Z
dc.descriptionLet $Q_n(x)=\sum_{i=0}^{n} A_{i}x^{i}$ be a random algebraic polynomial where the coefficients $A_0,A_1,... $ form a sequence of centered Gaussian random variables. Moreover, assume that the increments $Δ_j=A_j-A_{j-1}$, $j=0,1,2,...$ are independent, $A_{-1}=0$. 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 $Q_n(x)$ below level $u=O(n^k)$, for some $k>0$.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/math/0605116
dc.identifierhttp://arxiv.org/abs/math/0605116
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112655
dc.subjectProbability
dc.subject60H42; 60G99
dc.titleExpected Number of Local Maxima of Some Gaussian Random Polynomials
dc.typetext

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