PERFECT COCYCLES THROUGH STOCHASTIC DIFFERENTIAL-EQUATIONS

被引：52

作者：

ARNOLD, L ^{[1
]}

SCHEUTZOW, M ^{[1
]}

机构：

[1] TECH UNIV BERLIN,FACHBEREICH MATH,D-10623 BERLIN,GERMANY

来源：

PROBABILITY THEORY AND RELATED FIELDS | 1995年 / 101卷 / 01期

关键词：

Mathematics Subjects Classification: 60H10; 93E03;

D O I：

10.1007/BF01192196

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove that if phi is a random dynamical system (cocycle) for which t --> phi(t,omega)x is a semimartingale, then it is generated by a stochastic differential equation driven by a vector field valued semimartingale with stationary increments (helix), and conversely. This relation is succinctly expressed as ''semimartingale cocycle = exp(semimartingale helix)''. To implement it we lift stochastic calculus from the traditional one-sided time T = R(+) to two-sided time T = R and make this consistent with ergodic theory. We also prove a general theorem on the perfection of a crude cocycle, thus solving a problem which was open for more than ten years.

引用

页码：65 / 88

页数：24