Abstract
ANALYTICAL EXPECTATION OF NUMBER OF LEVEL CROSSINGS OF A RANDOM TRIGONOMETRIC POLYNOMIAL
Dr. P. K. Mishra* and Dipty Rani Dhal
ABSTRACT
The asymptotic estimates of the expected number of real zeros of thepolynomial T(? ) ?g1cos? ?g2cos2? ?......gncosn? wheregj(j=1,2,…..n) is a sequence of independent normally distributedrandom variables is such a number. To achieve the result we firstpresent a general formula for the covariance of the number of real zeros of any normalprocess, e(t), occurring in any two disjoint intervals. A formula for the variance of thenumber of real zeros of e(t) follows from this result.1991 Mathematics subject classification (Amer. Math. Soc.): 60 B 99.
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