Level crossings of a random trigonometric polynomial

Author:
Kambiz Farahmand

Journal:
Proc. Amer. Math. Soc. **111** (1991), 551-557

MSC:
Primary 60G99; Secondary 42A61

MathSciNet review:
1015677

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Abstract: This paper provides an asymptotic estimate for the expected number of -level crossings of the random trigonometric polynomial , where are independent normally distributed random variables with mean and variance one. It is shown that the result for remains valid for any finite constant and any such that as .

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1991-1015677-4

Keywords:
Number of real roots,
Kac-Rice formula,
random trigonometric polynomial

Article copyright:
© Copyright 1991
American Mathematical Society