ISSN (online) : 2395 - 7549

 
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5

Expected Number of Level Crossings of a Random Trigonometric Polynomial


Author(s):

Dr. Prasana Kumar Mishra , CET, BPUT ,BBSR; Dipty Rani Dhal, cet,bput,bbsr

Keywords:

Independent, Identically Distributed Random Variables, Random Algebraic Polynomial, Random Algebraic Equation, Real Roots, Domain of Attraction of the Normal Law, Slowly Varying Function

Abstract:

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
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