The two-dimensional stochastic heat equation: renormalizing a multiplicative noise

被引：29
|
作者：
Bertini, L
Cancrini, N
机构：
[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2BZ, England
[2] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy
[3] Ecole Polytech, Ctr Phys Theor, F-91128 Palaiseau, France
[4] Univ Roma La Sapienza, Dipartimento Fis, I-00185 Rome, Italy
来源：
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 1998年 / 31卷 / 02期
关键词：
D O I：
10.1088/0305-4470/31/2/019
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We study, in two space dimensions,the heat equation with a random potential that is a white noise in space and time. We introduce a regularization of the noise and prove that, by a suitable renormalization of the coupling coefficient, the covariance has a non-trivial limit when the regularization is removed. The limit is described in terms of a two-body Schrodinger operator with singular interaction.
引用
收藏
页码：615 / 622
页数：8
相关论文
共 50 条
  • [21] Estimating two-dimensional harmonics frequencies by extended matrix in multiplicative noise
    Wang, F
    Wang, SX
    Wu, YG
    ICEMI 2005: CONFERENCE PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON ELECTRONIC MEASUREMENT & INSTRUMENTS, VOL 1, 2005, : 470 - 474
  • [22] Large deviations for the two-dimensional stochastic Navier-Stokes equation with vanishing noise correlation
    Cerrai, Sandra
    Debussche, Arnaud
    ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2019, 55 (01): : 211 - 236
  • [23] Two-dimensional cubic nonlinear coupling estimation in correlative multiplicative noise
    Dou, HJ
    Wang, SX
    Wang, F
    PIMRC 2003: 14TH IEEE 2003 INTERNATIONAL SYMPOSIUM ON PERSONAL, INDOOR AND MOBILE RADIO COMMUNICATIONS PROCEEDINGS, VOLS 1-3 2003, 2003, : 2673 - 2677
  • [24] Stochastic resonance in two-dimensional Landau Ginzburg equation
    Benzi, R
    Sutera, A
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2004, 37 (32): : L391 - L398
  • [25] EXISTENCE AND ERGODICITY FOR THE TWO-DIMENSIONAL STOCHASTIC BOUSSINESQ EQUATION
    Li, Yong
    Trenchea, Catalin
    INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2018, 15 (4-5) : 715 - 728
  • [26] THE EXPONENTIAL BEHAVIOR OF THE STOCHASTIC PRIMITIVE EQUATIONS IN TWO DIMENSIONAL SPACE WITH MULTIPLICATIVE NOISE
    Medjo, Theodore Tachim
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2010, 14 (01): : 177 - 197
  • [27] Exact solutions for travelling waves using Tanh method for two dimensional stochastic Allen–Cahn equation with multiplicative noise
    Alzubaidi H.
    Journal of Umm Al-Qura University for Applied Sciences, 2025, 11 (1): : 153 - 158
  • [28] On the approximate controllability of a stochastic parabolic equation with a multiplicative noise
    Fernández-Cara, E
    Garrido-Atienza, MJ
    Real, J
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1999, 328 (08): : 675 - 680
  • [29] Large deviations for the stochastic quasigeostrophic equation with multiplicative noise
    Yang, Desheng
    Duan, Jinqiao
    JOURNAL OF MATHEMATICAL PHYSICS, 2010, 51 (05)
  • [30] A STOCHASTIC REACTION-DIFFUSION EQUATION WITH MULTIPLICATIVE NOISE
    FLANDOLI, F
    APPLIED MATHEMATICS LETTERS, 1991, 4 (04) : 45 - 48
12345