Large deviations of products of random topical operators

• 成果类型: Article
• 署名作者: Toomey, F
• 署名单位: Dublin Institute for Advanced Studies
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2002
• 页码: 317-333
• 关键词: Algebra

摘要

A topical operator on R-d is one which is isotone and homogeneous. Let {A(n) : n greater than or equal to 1} be a sequence of i.i.d. random topical operators such that the projective radius of A(n)...A(1) is almost surely bounded for large n. If {x (n) : n greater than or equal to 1} is a sequence of vectors given by x (n) = A (n)...A(1)x(0), for some fixed initial condition x(0), then the sequence {x(n)/n:n greater than or equal to 1} satisfies a weak large deviation principle. As corollaries of this result we obtain large deviation principles for products of certain random aperiodic max-plus and min-plus matrix operators and for products of certain random aperiodic nonnegative matrix operators.