Abstract
This paper provides an asymptotic estimate for the expected number
of level crossings of a trigonometric polynomial
This paper provides an asymptotic estimate for the expected number
of level crossings of a trigonometric polynomial
M. Kac, “On the average number of real roots of a random algebraic equation,” Bulletin of the American Mathematical Society, vol. 49, pp. 314–320, 1943.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. O. Rice, “Mathematical theory of random noise,” The Bell System Technical Journal, vol. 24, pp. 46–156, 1945.
View at: Google Scholar | Zentralblatt MATH | MathSciNetN. Wax, Ed., Selected Papers on Noise and Stochastic Processes, Dover, New York, NY, USA, 1954.
View at: Zentralblatt MATHJ. E. Wilkins Jr., “An asymptotic expansion for the expected number of real zeros of a random polynomial,” Proceedings of the American Mathematical Society, vol. 103, no. 4, pp. 1249–1258, 1988.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetI. Ibragimov and O. Zeitouni, “On roots of random polynomials,” Transactions of the American Mathematical Society, vol. 349, no. 6, pp. 2427–2441, 1997.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetK. Farahmand and J. M. Jahangiri, “Complex roots of a class of random algebraic polynomials,” Journal of Mathematical Analysis and Applications, vol. 226, no. 1, pp. 220–228, 1998.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetK. Farahmand, Topics in Random Polynomials, vol. 393 of Pitman Research Notes in Mathematics Series, Addison Wesley Longman, Harlow, UK, 1998.
View at: Zentralblatt MATH | MathSciNetA. Ramponi, “A note on the complex roots of complex random polynomials,” Statistics & Probability Letters, vol. 44, no. 2, pp. 181–187, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetK. Farahmand and A. Grigorash, “Complex zeros of algebraic polynomial with non-zero mean random coefficients,” Journal of Theoretical Probability, vol. 12, no. 4, pp. 1037–1044, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetP. Lakatos and L. Losonczi, “On zeros of reciprocal polynomials of odd degree,” Journal of Inequalities in Pure and Applied Mathematics, vol. 4, no. 3, p. 60, 2003.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. E. A. Dunnage, “The number of real zeros of a random trigonometric polynomial,” Proceedings of the London Mathematical Society, vol. 16, no. 1, pp. 53–84, 1966.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetK. Farahmand, “On the average number of level crossings of a random trigonometric polynomial,” The Annals of Probability, vol. 18, no. 3, pp. 1403–1409, 1990.
View at: Google Scholar | Zentralblatt MATH | MathSciNetK. Farahmand, “Number of real roots of a random trigonometric polynomial,” Journal of Applied Mathematics and Stochastic Analysis, vol. 5, no. 4, pp. 307–313, 1992.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetK. Farahmand, “On the number of real zeros of a random trigonometric polynomial: coefficients with nonzero infinite mean,” Stochastic Analysis and Applications, vol. 5, no. 4, pp. 379–386, 1987.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetA. T. Bharucha-Reid and M. Sambandham, Random Polynomials, Probability and Mathematical Statistics, Academic Press, Orlando, Fla, USA, 1986.
View at: Zentralblatt MATH | MathSciNetM. Das, “The number of real zeros of a class of random trigonometric polynomials,” The Mathematics Student, vol. 40, pp. 305–317, 1972.
View at: Google Scholar | MathSciNet