Rescaled contact processes converge to super-Brownian motion in two or more dimensions

被引：0

作者：

Richard Durrett

Edwin A. Perkins

机构：

[1] Department of Mathematics and ORIE,

[2] 278 Rhodes Hall,undefined

[3] Cornell University,undefined

[4] Ithaca,undefined

[5] NY 14853,undefined

[6] USA (e-mail: rtd1@cornell.edu),undefined

[7] Department of Mathematics,undefined

[8] 1984 Mathematics Rd.,undefined

[9] University of British Columbia,undefined

[10] Vancouver,undefined

[11] B.C. V6T 1Z2,undefined

[12] Canada (e-mail: perkins@math.ubc.ca),undefined

来源：

Probability Theory and Related Fields | 1999年 / 114卷

关键词：

Mathematics Subject Classification (1991): Primary 60K35, 60G57; Secondary: 60F05, 60J80;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We show that in dimensions two or more a sequence of long range contact processes suitably rescaled in space and time converges to a super-Brownian motion with drift. As a consequence of this result we can improve the results of Bramson, Durrett, and Swindle (1989) by replacing their order of magnitude estimates of how close the critical value is to 1 with sharp asymptotics.

引用

页码：309 / 399

页数：90

共 50 条

[31] Lattice trees and super-Brownian motion
Derbez, E
Slade, G
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1997, 40 (01): : 19 - 38
[32] The dimension of the boundary of super-Brownian motion
Mytnik, Leonid
Perkins, Edwin
PROBABILITY THEORY AND RELATED FIELDS, 2019, 174 (3-4) : 821 - 885
[33] The multifractal structure of super-Brownian motion
Perkins, EA
Taylor, SJ
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 1998, 34 (01): : 97 - 138
[34] The average density of super-Brownian motion
Mörters, P
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2001, 37 (01): : 71 - 100
[35] On the martingale problem for super-Brownian motion
Bass, RF
Perkins, EA
SEMINAIRE DE PROBABILITES XXXV, 2001, 1755 : 195 - 201
[36] The biodiversity of catalytic super-Brownian motion
Fleischmann, K
Klenke, A
ANNALS OF APPLIED PROBABILITY, 2000, 10 (04): : 1121 - 1136
[37] Thick points of super-Brownian motion
Jochen Blath
Peter Mörters
Probability Theory and Related Fields, 2005, 131 : 604 - 630
[38] Occupation time large deviations for critical, branching Brownian motion, super-Brownian motion and related processes
Deuschel, JD
Rosen, J
ANNALS OF PROBABILITY, 1998, 26 (02): : 602 - 643
[39] Kolmogorov's test for super-Brownian motion
Dhersin, JS
Le Gall, JF
ANNALS OF PROBABILITY, 1998, 26 (03): : 1041 - 1056
[40] Moderate deviation for super-Brownian motion with immigration
Mei Zhang
Science in China Series A: Mathematics, 2004, 47 : 440 - 452

← 1 2 3 4 5 →