Hitting times for the stochastic wave equation with fractional colored noise

被引：12

作者：

de la Cerda, Jorge Clarke ^{[1
,2
,3
]}

Tudor, Ciprian A. ^{[2
,4
]}

机构：

[1] Univ Bio Bio, Fac Ciencias, Dept Matemat, Concepcion, Chile

[2] Univ Lille 1, Lab Paul Painleve, F-59655 Villeneuve Dascq, France

[3] Univ Concepcion, Dept Ingn Matemat, CI MA 2, Concepcion, Chile

[4] Acad Econ Studies, Bucharest, Romania

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2014年 / 30卷 / 02期

关键词：

Stochastic wave equation; potential theory; hitting probability; capacity; Hausdorff dimension; spatially homogeneous Gaussian noise; fractional Brownian motion; Holder continuity; EVOLUTION-EQUATIONS; PROBABILITIES; DRIVEN; REGULARITY; DIMENSION; SYSTEMS;

D O I：

10.4171/RMI/796

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give sharp regularity results for the solution to the stochastic wave equation with linear fractional-colored noise. We apply these results in order to establish upper and lower bounds for the hitting probabilities of the solution in terms of the Hausdorff measure and the Newtonian capacity.

引用

页码：685 / 709

页数：25

共 50 条

[31] Gaussian fluctuations for the stochastic heat equation with colored noise
Huang, Jingyu
Nualart, David
Viitasaari, Lauri
Zheng, Guangqu
STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, 2020, 8 (02): : 402 - 421
[32] On weak convergence of stochastic heat equation with colored noise
Bezdek, Pavel
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2016, 126 (09) : 2860 - 2875
[33] TRANSPORTATION COST-INFORMATION INEQUALITY FOR A STOCHASTIC HEAT EQUATION DRIVEN BY FRACTIONAL-COLORED NOISE
李瑞囡
王新宇
Acta Mathematica Scientia, 2023, 43 (06) : 2519 - 2532
[34] Transportation cost-information inequality for a stochastic heat equation driven by fractional-colored noise
Ruinan Li
Xinyu Wang
Acta Mathematica Scientia, 2023, 43 : 2519 - 2532
[35] Transportation cost-information inequality for a stochastic heat equation driven by fractional-colored noise
Li, Ruinan
Wang, Xinyu
ACTA MATHEMATICA SCIENTIA, 2023, 43 (06) : 2519 - 2532
[36] Quadratic variations for the fractional-colored stochastic heat equation
Torres, Soledad
Tudor, Ciprian A.
Viens, Frederi G.
ELECTRONIC JOURNAL OF PROBABILITY, 2014, 19
[37] Hitting probabilities and hitting times for stochastic fluid flows
Bean, NG
O'Reilly, MM
Taylor, PG
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2005, 115 (09) : 1530 - 1556
[38] Small ball probabilities for the stochastic heat equation with colored noise
Chen, Jiaming
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2024, 177
[39] The Stochastic Heat Equation with Fractional-Colored Noise: Existence of the Solution (vol 4, pg 57, 2008)
Balan, Raluca M.
Tudor, Ciprian A.
ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2009, 6 : 343 - 347
[40] CHAOS EXPANSION AND REGULARITY OF THE LOCAL TIME OF THE SOLUTION TO THE STOCHASTIC HEAT EQUATION WITH ADDITIVE FRACTIONAL-COLORED NOISE
Tudor, Ciprian A.
TAIWANESE JOURNAL OF MATHEMATICS, 2013, 17 (05): : 1765 - 1777

← 1 2 3 4 5 →