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

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

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.