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BOUNDS OF THE NUMBER OF LEVEL CROSSINGS OF THE RANDOM ALGEBRAIC POLYNOMIALS

Abstract

In this paper we have estimate bounds of the number of level crossings of the random algebraic polynomials     n k k n k f x a t x 0 ( ,1) ( ) 0 where ak (t)  t,0  t 1, are dependent random variables assuming real values only and following the normal distribution with mean zero and joint density function M    M  a s (2 ) exp ( 1/ 2) ' 1/ 2 /   . There exists an integer n0 and a set E of measure at most A/(log n0log log log n0) such that, for each n>n0 and all not belonging to E, the equations (1.1) satisfying the condition (1.2), have at most (log log n) log n 2  roots where α and A are constants.

A.K. MANSINGH & DR. P.K.MISHRA

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