THE PACKING MEASURE OF THE RANGE OF SUPER-BROWNIAN MOTION

被引：2

作者：

Duquesne, Thomas ^{[1
]}

机构：

[1] Univ Paris 04, Lab Probabilites & Modeles Aleatoires, F-75252 Paris 05, France

来源：

ANNALS OF PROBABILITY | 2009年 / 37卷 / 06期

关键词：

Super-Brownian motion; Brownian Snake; range; exact packing measure; RANDOM TREE;

D O I：

10.1214/09-AOP468

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 the total range of Super-Brownian motion with quadratic branching mechanism has an exact packing measure with respect to the gauge function g(r) = r(4)(log log l/r)(-3) in super-critical dimensions d >= 5. More precisely, we prove that the total occupation measure of Super-Brownian motion is equal to the g-packing measure restricted to its range, up to a deterministic multiplicative constant that only depends on space dimension d.

引用

页码：2431 / 2458

页数：28

共 50 条

[21] Ergodic theorem for the two-dimensional super-Brownian motion with super-Brownian immigration [J].

Hong, WM .

PROGRESS IN NATURAL SCIENCE, 2000, 10 (02) :111-116

[22] The Hausdorff measure of the support of two-dimensional super-Brownian motion [J].

LeGall, JF ;

Perkins, EA .

ANNALS OF PROBABILITY, 1995, 23 (04) :1719-1747

[23] Killed rough super-Brownian motion [J].

Rosati, Tommaso Cornelis .

ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2020, 25 :1-12

[24] The dimension of the boundary of super-Brownian motion [J].

Leonid Mytnik ;

Edwin Perkins .

Probability Theory and Related Fields, 2019, 174 :821-885

[25] The extremal process of super-Brownian motion [J].

Ren, Yan-Xia ;

Song, Renming ;

Zhang, Rui .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2021, 137 :1-34

[26] An exit measure construction of the total local time of super-Brownian motion [J].

Hong, Jieliang .

ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2021, 26

[27] Lifetime and compactness of range for super-Brownian motion with a general branching mechanism [J].

Sheu, YC .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1997, 70 (01) :129-141

[28] ON THE BOUNDARY OF THE SUPPORT OF SUPER-BROWNIAN MOTION [J].

Mueller, Carl ;

Mytnik, Leonid ;

Perkins, Edwin .

ANNALS OF PROBABILITY, 2017, 45 (6A) :3481-3534

[29] Ergodic theorem for the two-dimensional super-Brownian motion with super-Brownian immigration [J].

洪文明 .

Progress in Natural Science, 2000, (02) :33-38

[30] The dimension of the boundary of super-Brownian motion [J].

Mytnik, Leonid ;

Perkins, Edwin .

PROBABILITY THEORY AND RELATED FIELDS, 2019, 174 (3-4) :821-885

← 1 2 3 4 5 →