J Austral Math Soc Ser A 58 pp39--46, 1995.

Level Crossings of a Random Trigonometric Polynomial with Dependent Coefficients

K. Farahmand

Abstract

This paper provides an asymptotic estimate for the expected number of K-level crossings of the random trigonometric polynomial g₁cosx + g₂cos2x + ¼+ g_ncosnx where g_j (j = 1, 2, ¼, n) are dependent normally distributed random variables with mean zero and variance one. The two cases of r_jr, the correlation coefficient between the j-th and r-th coefficients, being either (i) constant, or (ii) r^{|j - r|}j ¹ r, 0 < r < 1, are considered. It is shown that the previous result for r_jr = 0 still remains valid for both cases.

1991 AMS Subject Classification: primary 60G99; secondary 42BXX

Browse the article

Authors

K. Farahmand

Department of Mathematics, University of Ulster, Jordanstown, Co Antrim, BT37 OQB, United Kingdom.