Expected Number of Local Maxima of Some Gaussian Random Polynomials
| dc.creator | Shemehsavar, S. | |
| dc.creator | Rezakhah, S. | |
| dc.date | 2006-05-04 | |
| dc.date.accessioned | 2026-07-07T07:13:54Z | |
| dc.date.available | 2026-07-07T07:13:54Z | |
| dc.description | Let $Q_n(x)=\sum_{i=0}^{n} A_{i}x^{i}$ 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.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0605116 | |
| dc.identifier | http://arxiv.org/abs/math/0605116 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112655 | |
| dc.subject | Probability | |
| dc.subject | 60H42; 60G99 | |
| dc.title | Expected Number of Local Maxima of Some Gaussian Random Polynomials | |
| dc.type | text |