BROWNIAN MOTION AND THERMAL CAPACITY

被引：3

作者：

Khoshnevis, Davar ^{[1
]}

Xiao, Yimin ^{[2
]}

机构：

[1] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

[2] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA

来源：

ANNALS OF PROBABILITY | 2015年 / 43卷 / 01期

关键词：

Brownian motion; thermal capacity; Euclidean and space-time Hausdorff dimension; HAUSDORFF; SETS;

D O I：

10.1214/14-AOP910

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：

Let W denote d-dimensional Brownian motion. We find an explicit formula for the essential supremum of Hausdorff dimension of W (E) boolean AND F, where E subset of (0, infinity) and F subset of R-d are arbitrary nonrandom compact sets. Our formula is related intimately to the thermal capacity of Watson [Proc. Lond. Math. Soc. (3) 37 (1978) 342-362]. We prove also that when d >= 2, our formula can be described in terms of the Hausdorff dimension of E x F, where E x F is viewed as a subspace of space time.

引用

页码：405 / 434

页数：30

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