LEVEL-CROSSINGS OF A RANDOM POLYNOMIAL WITH HYPERBOLIC ELEMENTS

被引：5
|
作者：
FARAHMAND, K
机构：
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1995年 / 123卷 / 06期
关键词：
GAUSSIAN PROCESS; NUMBER OF REAL ROOTS; KAC-RICE FORMULA; ALGEBRAIC POLYNOMIALS; TRIGONOMETRIC POLYNOMIALS; FIXED PROBABILITY SPACE;
D O I：
10.2307/2161007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 +...+ g(n) cosh nx, where g(j) (j = 1,2,..., 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 = K-n = O(root n).
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页码：1887 / 1892
页数：6
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