NUMBER OF LEVEL CROSSINGS OF RANDOM ALGEBRAIC POLYNOMIALS

  • DR.P.K. MISHRA Department of Mathematics, College of Engineering and Technology AN AUTONOMOUS GOVT. COLLEGE Bhubaneswar, India
DOI: https://doi.org/10.53555/m.v5i2.2638
Keywords: Independent identically distributed random variables, random algebraic polynomial, random algebraic equation, real roots

Abstract

In this paper, we have estimated bounds of the number of level crossings of the random algebraic polynomials   where  are dependent random variables assuming real values only and following the normal distribution with mean zero and joint density function. There exists an integer n0 and a set E of measure at most such that, for each n>n0 and all not belonging to E, the equations (1.1) satisfying the condition (1.2), have at most roots where α and A are constants.

1991 Mathematics subject classification (Amer. Math. Soc.): 60 B 99.

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References

[1] Bharucha-Reid, A. and M. Sambandham (1986). Random Polynomials (Academic Press, New York).
[2] H. Cramer and M.R. Leadbetter. Stationary and Related Stochastic. Processes. (Wiley, New York)
[3] Dunnage, J.E.A. (1966). The number of real zeros of a random algebraic polynomial, Proc. London. Math. Soc. 16, 53-84.
[4] Dunnage, J.E.A. (1968). The number of real zeros of a class of random algebraic equation, Proc. London. Math. Soc. 18, 439-460.
[5] K. Farahmand. (1986). On the average number of real roots of a random algebraic equation. Ann. Probab. 14: 702-709.
Published
2019-03-02
How to Cite
MISHRA, D. (2019). NUMBER OF LEVEL CROSSINGS OF RANDOM ALGEBRAIC POLYNOMIALS. IJRDO -JOURNAL OF MATHEMATICS, 5(2), 37-45. https://doi.org/10.53555/m.v5i2.2638
Issue
Vol. 5 No. 2 (2019): IJRDO - Journal of Mathematics | ISSN: 2455-9210
Section
Articles

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