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