STOCHASTIC INTEGRATION OF PROCESSES WITH FINITE GENERALIZED VARIATIONS .1.

• 成果类型: Article
• 署名作者: TOWGHI, N
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988282
• 发表日期: 1995
• 页码: 629-667
• 关键词: linear measure-theory

摘要

In this paper the L(1)-stochastic integral and the mixed stochastic integral of a process Y with respect to a process X is defined in a way that extends Riemann-Stieltjes integration of deterministic functions with respect to X. The L(1)-integral will include the classical Ito integral. However, the concepts of ''filtration'' and adaptability do not play any role; instead, the p-variation of Dolean functions of the processes X and Y is the determining factor.