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] Adding interior points to an existing Brownian sheet lattice
Toth, D
STATISTICS & PROBABILITY LETTERS, 2004, 66 (03) : 221 - 227
[3] Brownian sheet and capacity
Khoshnevisan, D
Shi, Z
ANNALS OF PROBABILITY, 1999, 27 (03) : 1135 - 1159
[4] On the definition of a Brownian sheet
Alekseeva, Uliana Alekseevna
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2018, 24 (02): : 3 - 11
[5] Images of the Brownian sheet
Khoshnevisan, Davar
Xiao, Yimin
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 359 (07) : 3125 - 3151
[6] Zeros of the Brownian Sheet
Chen, Keming
Woessner, Guillaume
JOURNAL OF THEORETICAL PROBABILITY, 2025, 38 (02)
[7] Path Regularity of the Brownian Motion and the Brownian Sheet
Kempka, H.
Schneider, C.
Vybiral, J.
CONSTRUCTIVE APPROXIMATION, 2024, 59 (02) : 485 - 539
[8] Path Regularity of the Brownian Motion and the Brownian Sheet
H. Kempka
C. Schneider
J. Vybiral
Constructive Approximation, 2024, 59 : 485 - 539
[9] QUASI-EVERYWHERE PROPERTIES OF BROWNIAN LEVEL SETS AND MULTIPLE POINTS
PENROSE, MD
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1990, 36 (01) : 33 - 43
[10] The reassembling of shattered Brownian sheet
Pyke, R
STATE OF THE ART IN PROBABILITY AND STATISTICS: FESTSCHRIFT FOR WILLEM R VAN ZWET, 2001, 36 : 518 - 532

← 1 2 3 4 5 →