POLARITY OF POINTS FOR GAUSSIAN RANDOM FIELDS

被引：12

作者：

Dalang, Robert C. ^{[1
]}

Mueller, Carl ^{[2
]}

Xiao, Yimin ^{[3
]}

机构：

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

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

[3] Michigan State Univ, Dept Stat & Probabil, A-413 Wells Hall, E Lansing, MI 48824 USA

来源：

ANNALS OF PROBABILITY | 2017年 / 45卷 / 6B期

基金：

美国国家科学基金会;

关键词：

Hitting probabilities; polarity of points; critical dimension; harmonizable representation; stochastic partial differential equations; STOCHASTIC HEAT-EQUATIONS; HITTING PROBABILITIES; BROWNIAN SHEET; HAUSDORFF MEASURE; MULTIPLE POINTS; SYSTEMS; TRAJECTORIES; DIMENSION; DRIVEN; TIMES;

D O I：

10.1214/17-AOP1176

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 show that for a wide class of Gaussian random fields, points are polar in the critical dimension. Examples of such random fields include solutions of systems of linear stochastic partial differential equations with deterministic coefficients, such as the stochastic heat equation or wave equation with space-time white noise, or colored noise in spatial dimensions k >= 1. Our approach builds on a delicate covering argument developed by M. Talagrand [Ann. Probab. 23 (1995) 767-775; Probab. Theory Related Fields 112 (1998) 545-563] for the study of fractional Brownian motion, and uses a harmonizable representation of the solutions of these stochastic PDEs.

引用

页码：4700 / 4751

页数：52

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