Number of Level Crossings of a Random Trigonometric Polynomial

Authors

  • Prasana Kumar Mishra

Keywords:

Level crossings,, trigonometric functions independent, identically distributed random variables, random algebraic polynomial, random algebraic equation, real roots, domain of attraction of the normal law, slowly varying function

Abstract

The asymptotic estimates of the expected number of real zeros of the polynomial.  gj (j=1, 2, n) is a sequence of independent normally distributed random variables is such a number. To achieve the result we first present a general formula for the covariance of the number of real zeros of any normal process, e (t), occurring in any two disjoint intervals. A formula for the variance of the number of real zeros of e (t) follows from this result.

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Published

2015-06-20

Issue

Vol. 1 No. 1,2,3 (2015)

Section

Articles