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Research Article Open Access
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 n0log 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.
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Author(s): A.K. MANSINGH & DR. P.K.MISHRA