## Level crossings of a random polynomial with hyperbolic elements

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- by K. Farahmand PDF
- Proc. Amer. Math. Soc.
**123**(1995), 1887-1892 Request permission

## Abstract:

This paper provides an asymptotic estimate for the expected number of*K*-level crossings of a random hyperbolic polynomial ${g_1}\cosh x + {g_2}\cosh 2x + \cdots + {g_n}\cosh nx$, where ${g_j}(j = 1,2, \ldots ,n)$ are independent normally distributed random variables with mean zero, variance one and

*K*is any constant independent of

*x*. It is shown that the result for $K = 0$ remains valid as long as $K \equiv {K_n} = O(\sqrt n )$.

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## Additional Information

- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**123**(1995), 1887-1892 - MSC: Primary 60H99; Secondary 42A05
- DOI: https://doi.org/10.1090/S0002-9939-1995-1264810-1
- MathSciNet review: 1264810