Journal of Computational Mathematics and Applied Mathematics

Authors:-Dr. P. K. Mishra*, Debasis Gountia

Abstract:-

In this paper, we have estimated 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) ï‚£ t,0 ï‚£ t ï‚£1, are dependent random variables assuming real values
only and following the normal distribution with mean zero and joint density
function M ï° ï› ï¤ Mï¤ ï 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 ï¡ roots where α and A are constants.
1991 Mathematics subject classification (Amer. Math. Soc.): 60 B 99.