Space-time fractional Anderson model driven by Gaussian noise rough in space

被引：1
作者：
Liu, Junfeng [1 ]
Wang, Zhi [2 ]
Wang, Zengwu [3 ]
机构：
[1] Nanjing Audit Univ, Sch Stat & Data Sci, Nanjing 211815, Peoples R China
[2] Ningbo Univ Technol, Sch Sci, Ningbo 315211, Peoples R China
[3] Chinese Acad Social Sci, Inst Finance & Banking, Beijing 100710, Peoples R China
来源：
STOCHASTICS AND DYNAMICS | 2023年 / 23卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Space-time fractional Anderson model; Gaussian noise; Malliavin calculus; moment bounds; Holder continuity; STOCHASTIC HEAT-EQUATION; INTERMITTENCY; EXCITATION; PRINCIPLE; WAVE;
D O I：
10.1142/S021949372350003X
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 paper, we study a class of space-time fractional Anderson model driven by multiplicative Gaussian noise which is white/colored in time and has the covariance of a fractional Brownian motion with Hurst index H < 1/2 in space. We prove the existence of the solution in the Skorohod sense and obtain the upper and lower bounds for the pth moments for all p >= 2. Then we can prove that solution of this equation in the Skorohod sense is weakly intermittent. We also deduce the Holder continuity of the solution with respect to the time and space variables.
引用
收藏
页数：31
相关论文
共 50 条
  • [1] Moment Bounds for a Generalized Anderson Model with Gaussian Noise Rough in Space
    Liu, Junfeng
    JOURNAL OF THEORETICAL PROBABILITY, 2023, 36 (01) : 167 - 200
  • [2] Parabolic Anderson Model with Space-Time Homogeneous Gaussian Noise and Rough Initial Condition
    Balan, Raluca M.
    Chen, Le
    JOURNAL OF THEORETICAL PROBABILITY, 2018, 31 (04) : 2216 - 2265
  • [3] High order Anderson parabolic model driven by rough noise in space
    Cao, Qiyong
    Gao, Hongjun
    STOCHASTICS AND DYNAMICS, 2022, 22 (01)
  • [4] Hyperbolic Anderson Model with space-time homogeneous Gaussian noise
    Balan, Raluca M.
    Song, Jian
    ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2017, 14 (02): : 799 - 849
  • [5] Parabolic Anderson Model with Space-Time Homogeneous Gaussian Noise and Rough Initial Condition
    Raluca M. Balan
    Le Chen
    Journal of Theoretical Probability, 2018, 31 : 2216 - 2265
  • [6] Fractional stochastic wave equation driven by a Gaussian noise rough in space
    Song, Jian
    Song, Xiaoming
    Xu, Fangjun
    BERNOULLI, 2020, 26 (04) : 2699 - 2726
  • [7] Moment Bounds for a Generalized Anderson Model with Gaussian Noise Rough in Space
    Junfeng Liu
    Journal of Theoretical Probability, 2023, 36 : 167 - 200
  • [8] Intermittency for the Hyperbolic Anderson Model with rough noise in space
    Balan, Raluca M.
    Jolis, Maria
    Quer-Sardanyons, Lluis
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2017, 127 (07) : 2316 - 2338
  • [9] Fractional Kinetic Equation Driven by General Space-Time Homogeneous Gaussian Noise
    Liu, Junfeng
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2019, 42 (06) : 3475 - 3499
  • [10] HOLDER CONTINUITY FOR THE PARABOLIC ANDERSON MODEL WITH SPACE-TIME HOMOGENEOUS GAUSSIAN NOISE
    Balan, Raluca M.
    Quer-Sardanyons, Lluis
    Song, Jian
    ACTA MATHEMATICA SCIENTIA, 2019, 39 (03) : 717 - 730
12345