期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2001
卷号：25
DOI：10.1155/S016117120100391X
出版社：Hindawi Publishing Corporation
摘要：We present a useful formula for the expected number of maxima of a
normal process ξ(t) that occur below a level u. In the
derivation we assume chiefly that ξ(t),ξ′(t), and ξ′′(t) have, with probability one, continuous 1 dimensional
distributions and expected values of zero. The formula referred to
above is then used to find the expected number of maxima below the
level u for the random algebraic polynomial. This result
highlights the very pronounced difference in the behaviour of the
random algebraic polynomial on the interval (−1,1) compared with
the intervals (−∞,−1) and (1,∞). It is also shown
that the number of maxima below the zero level is no longer O(logn) on the intervals (−∞,−1) and (1,∞).
