International Journal of Stochastic Analysis
Volume 2010 (2010), Article ID 931565, 10 pages
doi:10.1155/2010/931565
Research Article

Random Trigonometric Polynomials with Nonidentically Distributed Coefficients

K. Farahmand and T. Li

Department of Mathematics, University of Ulster at Jordanstown, Co. Antrim, BT37 0QB, UK

Received 17 December 2009; Accepted 9 February 2010

Academic Editor: Bradford Allen

Copyright © 2010 K. Farahmand and T. Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. E. A. Dunnage, “The number of real zeros of a random trigonometric polynomial,” Proceedings of the London Mathematical Society, vol. 16, pp. 53–84, 1966. View at Zentralblatt MATH · View at MathSciNet
  2. K. 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 · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. K. Farahmand, “Level crossings of a random trigonometric polynomial,” Proceedings of the American Mathematical Society, vol. 111, no. 2, pp. 551–557, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. K. 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 · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. M. Sambandham and N. Renganathan, “On the number of real zeros of a random trigonometric polynomial: coefficients with nonzero mean,” The Journal of the Indian Mathematical Society, vol. 45, no. 1–4, pp. 193–203, 1981. View at MathSciNet
  6. K. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. A. T. Bharucha-Reid and M. Sambandham, Random Polynomials, Probability and Mathematical Statistics, Academic Press, Orlando, Fla, USA, 1986. View at Zentralblatt MATH · View at MathSciNet
  8. K. Farahmand and M. Sambandham, “On the expected number of real zeros of random trigonometric polynomials,” Analysis, vol. 17, no. 4, pp. 345–353, 1997. View at Zentralblatt MATH · View at MathSciNet
  9. K. Farahmand, “On zeros of self-reciprocal random algebraic polynomials,” Journal of Applied Mathematics and Stochastic Analysis, vol. 2007, Article ID 43091, 7 pages, 2007. View at Zentralblatt MATH · View at MathSciNet
  10. K. Farahmand, Topics in Random Polynomials, vol. 393 of Pitman Research Notes in Mathematics Series, Addison Wesley Longman, London, UK, 1998. View at MathSciNet
  11. E. C. Titchmarsh, The Theory of Functions, Oxford University Press, Oxford, UK, 1939.