| Title | ALGEBRAIC POLYNOMIALS WITH DEPENDENT RANDOM COEFFICIENTS |
| Publication Type | Journal Article |
| Year of Publication | 2005 |
| Authors | Farahmand, K |
| Secondary Authors | Nezakati, A |
| Secondary Title | Communications in Applied Analysis |
| Volume | 9 |
| Issue | 1 |
| Start Page | 94 |
| Pagination | 104 |
| Date Published | 01/2005 |
| Type of Work | scientific: mathematics |
| ISSN | 1083–2564 |
| AMS | 42BXX, 60H99 |
| Abstract | This paper provides an asymptotic estimate for the expected number of real zeros of a random algebraic polynomial a0 + a1x + a2x2 + · · · + an−1xn−1. The coefficients ai (i = 0, 1, 2, · · · , n − 1) are assumed to be dependent normal random variables with correlation coefficients of any two terms i and j,
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| URL | http://www.acadsol.eu/en/articles/9/1/6.pdf |
| Short Title | Algebraic Polynomials with Dependent Random Coefficients |
| Refereed Designation | Refereed |
| Full Text | REFERENCES[1] A.T. Bharucha-Reid and M. Sambandham, Random Polynomials, Academic Press, N.Y., 1986.
[2] K. Farahmand, Topics in Random Polynomials, Addison Wesley Longman, London, 1998. [3] M. Kac, On the average number of real roots of a random algebraic equation, Bull. Amer. Math. Soc., 49 (1943), 314–320. [4] B.F. Logan and L.A. Shepp, Real zeros of random polynomials, Proc. London Math. Soc., 18 (1968), 29–35. [5] B.F. Logan and L.A. Shepp, Real zeros of random polynomials, II, Proc. London Math. Soc., 18 (1968), 308–314. [6] C. Newman, Asymptotic independence and limit theorems for positively and negatively dependent random variables, Inequalities in Statistics and Probability. IMS Lecture Notes-Monograhp Series, 5 (1984), 127–140. [7] N. Renganathan and M. Sambandham, On the average number of real zeros of a random trigonometric polynomial with dependent coefficients-II, Indian J. Pure Appl. Math., 15 (1984), 951–956. [8] M. Sambandham, On a random algebraic polynomial, J. Indian Math. Soc., 41 (1977), 83–97. [9] M. Sambandham, On the number of real zeros of a random trigonometric polynomial, Trans. Amer. Math. Soc., 238 (1978), 57–70.
[10] M. Sambandham, On the upper bound of the number of real roots of a random algebraic equation, J. Indian Math. Soc., 42 (1978), 15–26. [11] M. Sambandham, On the average number of real zeros of a class of random algebraic curves, Pacific J. Math., 81 (1979), 207–215. [12] J.E. Wilkins, An asymptotic expansion for the expected number of real zeros of a random polynomial, Proc. Amer. Math. Soc., 103 (1988), 1249–1258. |
assumed ρij = −ρ|i−j|, where ρ is any positive constant in the interval (0, 1/3). Previous results are mainly for independent distributed coefficients or for a positive correlation coefficient in (0, 1/2).