Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise

被引：3

作者：

Chakraborty, Prakash ^{[1
]}

Chen, Xia ^{[2
]}

Gao, Bo ^{[2
]}

Tindel, Samy ^{[3
]}

机构：

[1] Purdue Univ, Dept Stat, 150 N Univ St, W Lafayette, IN 47907 USA

[2] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

[3] Purdue Univ, Dept Math, 150 N Univ St, W Lafayette, IN 47907 USA

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2020年 / 130卷 / 11期

关键词：

Stochastic heat equation; Parabolic Anderson model; Fractional Brownian motion; Feynman-Kac formula; Lyapounov exponent; BROWNIAN-MOTION;

D O I：

10.1016/j.spa.2020.06.007

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：

In this note we consider the parabolic Anderson model in one dimension with time-independent fractional noise (W)over dot in space. We consider the case H < 1/2 and get existence and uniqueness of solution. In order to find the quenched asymptotics for the solution we consider its Feynman-Kac representation and explore the asymptotics of the principal eigenvalue for a random operator of the form 1/2 Delta + (W)over dot. (C) 2020 Elsevier B.V. All rights reserved.

引用

页码：6689 / 6732

页数：44

共 50 条

[31] STOCHASTIC HEAT EQUATION WITH ROUGH DEPENDENCE IN SPACE
Hu, Yaozhong
Huang, Jingyu
Le, Khoa
Nualart, David
Tindel, Samy
ANNALS OF PROBABILITY, 2017, 45 (6B): : 4561 - 4616
[32] NONLINEAR STOCHASTIC HEAT EQUATION DRIVEN BY SPATIALLY COLORED NOISE: MOMENTS AND INTERMITTENCY
Chen, Le
Kim, Kunwoo
ACTA MATHEMATICA SCIENTIA, 2019, 39 (03) : 645 - 668
[33] NONLINEAR STOCHASTIC HEAT EQUATION DRIVEN BY SPATIALLY COLORED NOISE:MOMENTS AND INTERMITTENCY
陈乐
Kunwoo KIM
Acta Mathematica Scientia, 2019, 39 (03) : 645 - 668
[34] The fractional stochastic heat equation driven by time-space white noise
Moulay Hachemi R.Y.
Øksendal B.
Fractional Calculus and Applied Analysis, 2023, 26 (2) : 513 - 532
[35] Nonlinear Stochastic Heat Equation Driven by Spatially Colored Noise: Moments and Intermittency
Le Chen
Kunwoo Kim
Acta Mathematica Scientia, 2019, 39 : 645 - 668
[36] SOME STABILITY RESULTS FOR SEMILINEAR STOCHASTIC HEAT EQUATION DRIVEN BY A FRACTIONAL NOISE
El Barrimi, Oussama
Ouknine, Youssef
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2019, 56 (03) : 631 - 648
[37] Numerical Solution of 1-D DPL Heat Transfer Equation
Raszkowski, Tomasz
Zubert, Mariusz
Janicki, Marcin
Napieralski, Andrzej
2015 22ND INTERNATIONAL CONFERENCE MIXED DESIGN OF INTEGRATED CIRCUITS & SYSTEMS (MIXDES), 2015, : 436 - 439
[38] Irreducibility and Asymptotics of Stochastic Burgers Equation Driven by α-stable Processes
Dong, Zhao
Wang, Feng-Yu
Xu, Lihu
POTENTIAL ANALYSIS, 2020, 52 (03) : 371 - 392
[39] A link between the cost of fast controls for the 1-D heat equation and the uniform controllability of a 1-D transport-diffusion equation
Lissy, Pierre
COMPTES RENDUS MATHEMATIQUE, 2012, 350 (11-12) : 591 - 595
[40] Irreducibility and Asymptotics of Stochastic Burgers Equation Driven by α-stable Processes
Zhao Dong
Feng-Yu Wang
Lihu Xu
Potential Analysis, 2020, 52 : 371 - 392

← 1 2 3 4 5 →