Expected Number of Slope Crossings of Certain Gaussian Random Polynomials
| dc.creator | Rezakhah, S. | |
| dc.creator | Shemehsavar, S. | |
| dc.date | 2006-12-31 | |
| dc.date.accessioned | 2026-07-07T08:08:33Z | |
| dc.date.available | 2026-07-07T08:08:33Z | |
| dc.description | Let $Q_n(x)=\sum_{i=0}^{n} A_{i}x^{i}$ be a random 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 study the number of times that such a random polynomial crosses a line which is not necessarily parallel to the x-axis. More precisely we obtain the asymptotic behavior of the expected number of real roots of the equation $Q_n(x)=Kx$, for the cases that $K$ is any non-zero real constant $K=o(n^{1/4})$, and $K=o(n^{1/2})$ separately. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701019 | |
| dc.identifier | http://arxiv.org/abs/math/0701019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131299 | |
| dc.subject | Probability | |
| dc.subject | Statistics Theory | |
| dc.subject | 60H42, 60G99 | |
| dc.title | Expected Number of Slope Crossings of Certain Gaussian Random Polynomials | |
| dc.type | text |