Stochastic integrals: A combinatorial approach

• 成果类型: Article
• 署名作者: Rota, GC; Wallstrom, TC
• 署名单位: Massachusetts Institute of Technology (MIT); United States Department of Energy (DOE); Los Alamos National Laboratory; Catholic University of America
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1997
• 页码: 1257-1283
• 关键词: foundations; calculus

摘要

A combinatorial definition of multiple stochastic integrals is given in the setting of random measures. It is shown that some properties of such stochastic integrals, formerly known to hold in special cases, are instances of combinatorial identities on the lattice of partitions of a set. The notion of stochastic sequences of binomial type is introduced as a generalization of special polynomial sequences occuring in stochastic integration, such as Hermite, Poisson-Charlier and Kravchuk polynomials. It is shown that identities for such polynomial sets have a common origin.