Farahmand, K. Number of real roots of a random trigonometric polynomial. (English) Zbl 0770.60055 J. Appl. Math. Stochastic Anal. 5, No. 4, 307-313 (1992). Summary: We study the expected number of real roots of the random equation \[ g_ 1\cos\theta+g_ 2\cos 2\theta+\cdots+g_ n\cos n\theta=K, \] where the coefficients \(g_ j\)’s are normally distributed, but not necessarily all identical. It is shown that although this expected number is independent of the means of \(g_ j\), \(j=1,2,\dots,n\), it will depend on their variances. The previous works in this direction considered the identical distribution for the coefficients. Cited in 3 Documents MSC: 60G99 Stochastic processes 42B99 Harmonic analysis in several variables Keywords:number of level crossings; random trigonometric polynomial; Kac-Rice formula; expected number of real roots PDFBibTeX XMLCite \textit{K. Farahmand}, J. Appl. Math. Stochastic Anal. 5, No. 4, 307--313 (1992; Zbl 0770.60055) Full Text: DOI EuDML