On the Average Number of Sharp Crossings of Certain Gaussian Random Polynomials
| dc.creator | Shemehsavar, S. | |
| dc.creator | Rezakhah, S. | |
| dc.date | 2006-05-27 | |
| dc.date.accessioned | 2026-07-07T08:07:52Z | |
| dc.date.available | 2026-07-07T08:07:52Z | |
| 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, assuming $A_{-1}=0$. The coefficients can be considered as $n$ consecutive observations of a Brownian motion. We obtain the asymptotic behaviour of the expected number of u-sharp crossings of polynomial $Q_n(x)$ . We refer to u-sharp crossings as those zero up-crossings with slope greater than $u$, or those down-crossings with slope smaller than $-u$. We consider the cases where $u$ is unbounded and is increasing with $n$, where $u=o(n^{5/4})$, and $u=o(n^{3/2})$ separately. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0605699 | |
| dc.identifier | http://arxiv.org/abs/math/0605699 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131074 | |
| dc.subject | Probability | |
| dc.subject | Statistics Theory | |
| dc.subject | 60H42; 60G99 | |
| dc.title | On the Average Number of Sharp Crossings of Certain Gaussian Random Polynomials | |
| dc.type | text |