Expected Number of Level Crossings of a Random Trigonometric Polynomial
Author(s):
Dr. Prasana Kumar Mishra , CET, BPUT ,BBSR; Dipty Rani Dhal, cet,bput,bbsrKeywords:
Independent, Identically Distributed Random Variables, Random Algebraic Polynomial, Random Algebraic Equation, Real Roots, Domain of Attraction of the Normal Law, Slowly Varying FunctionAbstract:
Let EN( T; Φ’ , Φ’’ ) denote the average number of real zeros of the random trigonometric polynomial T=Tn( Φ, ω )= . In the interval (Φ’, Φ’’). Assuming that ak(ω ) are independent random variables identically distributed according to the normal law and that bk = kp (p ≥ 0) are positive constants, we show that EN( T : 0, 2π ) ~ Outside an exceptional set of measure at most (2/ n ) where β = constant S ~ 1, S’ ~ 1. 1991 Mathematics subject classification (amer. Math. Soc.): 60 B 99.
Other Details:
| Manuscript Id | : | J4RV1I12014 |
| Published in | : | Volume : 1, Issue : 12 |
| Publication Date | : | 01/03/2016 |
| Page(s) | : | 37-40 |
