NON-MARKOVIAN INVARIANT-MEASURES ARE HYPERBOLIC

被引：12

作者：

CRAUEL, H

机构：

[1] Fachbereich 9 Mathematik, Universität des Saarlandes, Saarbrücken

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1993年 / 45卷 / 01期

关键词：

D O I：

10.1016/0304-4149(93)90057-B

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：

Suppose mu is an invariant measure for a smooth random dynamical system on a d-dimensional Riemannian manifold. We prove that alpha(mu) less-than-or-equal-to dE(mu)(max{0, -lambda(d)mu}), where alpha(mu) is the relative entropy of mu, lambda(d)mu is the smallest Lyapunov exponent associated with mu, and E(mu) denotes integration with respect to mu.

引用

页码：13 / 28

页数：16

共 15 条

[1]

BAXENDALE P, 1989, PROBAB THEORY REL, V81, P522

[2]

Bougerol P., 1985, PRODUCTS RANDOM MATR

[3]

Crauel H., 1991, Stochastics and Stochastics Reports, V37, P153, DOI 10.1080/17442509108833733

[4]

CRAUEL H, 1991, LECT NOTES MATH, V1486, P38

[5]

CRAUEL H, 1987, THESIS U BREMEN BREM

[6]

CRAUEL H, 1990, J DYNAMICS DIFFERENT, V2, P245

[7]

Gromov M., 1986, PARTIAL DIFFERENTIAL

[8]

KIFER Y, 1988, LECT NOTES MATH, V1325, P125

[9]

KINGMAN JFC, 1968, J ROY STAT SOC B, V30, P499

[10]

KLINGENBERG W, 1982, RIEMANNIAN GEOMETRY

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