MULTIPLE POINTS OF THE BROWNIAN SHEET IN CRITICAL DIMENSIONS

被引：6

作者：

Dalang, Robert C. ^{[1
]}

Mueller, Carl ^{[2
]}

机构：

[1] Ecole Polytech Fed Lausanne, Inst Math, Stn 8, CH-1015 Lausanne, Switzerland

[2] Univ Rochester, Dept Math, Rochester, NY 14627 USA

来源：

ANNALS OF PROBABILITY | 2015年 / 43卷 / 04期

关键词：

Brownian sheet; multiple points; Girsanov's theorem;

D O I：

10.1214/14-AOP912

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：

It is well known that an N-parameter d-dimensional Brownian sheet has no k-multiple points when (k - 1)d > 2kN, and does have such points when (k - 1)d < 2kN. We complete the study of the existence of k-multiple points by showing that in the critical cases where (k - 1)d = 2kN, there are a.s. no k-multiple points.

引用

页码：1577 / 1593

页数：17

共 50 条

[1] CRITICAL BROWNIAN SHEET DOES NOT HAVE DOUBLE POINTS
Dalang, Robert C.
Khoshnevisan, Davar
Nualart, Eulalia
Wu, Dongsheng
Xiao, Yimin
ANNALS OF PROBABILITY, 2012, 40 (04): : 1829 - 1859
[2] Points of increase of the Brownian sheet
Dalang, RC
Mountford, T
PROBABILITY THEORY AND RELATED FIELDS, 1997, 108 (01) : 1 - 27
[3] Points of increase of the Brownian sheet
Robert C. Dalang
T. Mountford
Probability Theory and Related Fields, 1997, 108 : 1 - 27
[4] A critical case for Brownian slow points
Probab Theory Relat Fields, 1 (85):
[5] A critical case for Brownian slow points
Bass, RF
Burdzy, K
PROBABILITY THEORY AND RELATED FIELDS, 1996, 105 (01) : 85 - 108
[6] BROWNIAN SLOW POINTS - THE CRITICAL CASE
DAVIS, B
PERKINS, E
ANNALS OF PROBABILITY, 1985, 13 (03): : 779 - 803
[7] Adding interior points to an existing Brownian sheet lattice
Toth, D
STATISTICS & PROBABILITY LETTERS, 2004, 66 (03) : 221 - 227
[8] CRITICAL POINTS IN 3 DIMENSIONS
ROSENSTOCK, HB
JOURNAL OF PHYSICS AND CHEMISTRY OF SOLIDS, 1957, 2 (01) : 44 - 54
[9] MULTIPLE POINTS OF PATHS OF BROWNIAN MOTION IN THE PLANE
DVORETZKY, A
ERDOS, P
KAKUTANI, S
ANNALS OF MATHEMATICAL STATISTICS, 1954, 25 (02): : 410 - 410
[10] ON MULTIPLE POINTS OF PLANAR BROWNIAN-MOTION
LEGALL, JF
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1984, 299 (13): : 627 - 630

← 1 2 3 4 5 →