TY - JOUR
T1 - On Classifications of Random Polynomials
TT - در بارهی ردهبندیهای چندجملهایهای تصادفی
JF - srtc-jsri
JO - srtc-jsri
VL - 1
IS - 1
UR - http://jsri.srtc.ac.ir/article-1-135-en.html
Y1 - 2004
SP - 1
EP - 12
KW - number of real zeros
KW - real roots
KW - random algebraic polynomials
KW - trigonometric polynomials
KW - binomial coefficients
KW - Kac-Rice formula
KW - non-identical random variables
KW - complex roots.
N2 - Let $ a_0 (omega), a_1 (omega), a_2 (omega), dots, a_n (omega)$ be a sequence of independent random variables defined on a fixed probability space $(Omega, Pr, A)$. There are many known results for the expected number of real zeros of a polynomial $ a_0 (omega) psi_0(x)+ a_1 (omega)psi_1 (x)+, a_2 (omega)psi_2 (x)+ dots + a_n (omega)psi_n (x)$ where $ psi_j(x)$ , j=0.1.2...,n is a specific function of x. In this paper we highlight different characteristics arising for the random polynomial dictated by assuming different values for $ psi_j(x)$. Then we are able to classify random polynomials into three classes each of which share common properties. Although, we are mainly concerned with the number of real roots we also study the density of complex roots generated by assuming complex random coefficients for polynomials.
M3 10.18869/acadpub.jsri.1.1.1
ER -