首页    期刊浏览 2025年06月10日 星期二
登录注册

文章基本信息

  • 标题:Local maxima of a random algebraic polynomial
  • 本地全文:下载
  • 作者:K. Farahmand ; P. Hannigan
  • 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
  • 期号:5
  • 页码:331-343
  • 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 ( log n ) on the intervals ( − ∞ , − 1 ) and ( 1 , ∞ ) .

国家哲学社会科学文献中心版权所有