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

[21] Non-independence of excursions of the Brownian sheet and of additive Brownian motion
Dalang, RC
Mountford, T
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 355 (03) : 967 - 985
[22] Degree two Brownian Sheet in Dimension three
Jérôme Depauw
Probability Theory and Related Fields, 2006, 135 : 457 - 469
[23] Some Polar Sets for the Generalized Brownian Sheet
LI Huiqiong1
2.School of Mathematics and Statistics
Wuhan University Journal of Natural Sciences, 2008, (02) : 137 - 140
[24] Eccentric behaviors of the Brownian sheet along lines
Dalang, RC
Mountford, T
ANNALS OF PROBABILITY, 2002, 30 (01) : 293 - 322
[25] Degree two Brownian sheet in dimension three
Depauw, J
PROBABILITY THEORY AND RELATED FIELDS, 2006, 135 (03) : 457 - 469
[26] Weak approximation of the complex Brownian sheet from a Levy sheet and applications to SPDEs
Bardina, Xavier
Pablo Marquez, Juan
Quer-Sardanyons, Lluis
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2020, 130 (09) : 5735 - 5767
[27] Random walk local time approximated by a Brownian sheet combined with an independent Brownian motion
Csaki, Endre
Csoergo, Miklos
Foeldes, Antonia
Revesz, Pal
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2009, 45 (02): : 515 - 544
[28] A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion.
Baker, D.
Yor, M.
ELECTRONIC JOURNAL OF PROBABILITY, 2009, 14 : 1532 - 1540
[29] Slices of a Brownian sheet: New results and open problems
Khoshnevisan, Davar
SEMINAR ON STOCHASTIC ANALYSIS, RANDOM FIELDS AND APPLICATIONS V, 2008, 59 : 135 - 174
[30] Rate of convergence of uniform transport processes to a Brownian sheet
Rovira, Carles
OPEN MATHEMATICS, 2020, 18 : 731 - 737

← 1 2 3 4 5 →