On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients

被引：49

作者：

Mytnik, Leonid ^{[1
]}

Perkins, Edwin

Sturm, Anja

机构：

[1] Technion Israel Inst Technol, Fac Ind Engn & Management, IL-32000 Haifa, Israel

[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

[3] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

来源：

ANNALS OF PROBABILITY | 2006年 / 34卷 / 05期

关键词：

heat equation; colored noise; stochastic partial differential equation; uniqueness; existence;

D O I：

10.1214/009117906000000331

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 consider the existence and pathwise uniqueness of the stochastic heat equation with a multiplicative colored noise term on R-d for d >= 1. We focus on the case of non-Lipschitz noise coefficients and singular spatial noise correlations. In the course of the proof a new result on Holder continuity of the solutions near zero is established.

引用

页码：1910 / 1959

页数：50

共 50 条

[31] PATHWISE UNIQUENESS OF THE STOCHASTIC HEAT EQUATION WITH SPATIALLY INHOMOGENEOUS WHITE NOISE
Neuman, Eyal
ANNALS OF PROBABILITY, 2018, 46 (06) : 3090 - 3187
[32] Discrete fractional Bihari inequality and uniqueness theorem of solutions of nabla fractional difference equations with non-Lipschitz nonlinearities
Wang, Mei
Jia, Baoguo
Chen, Churong
Zhu, Xiaojuan
Du, Feifei
APPLIED MATHEMATICS AND COMPUTATION, 2020, 376
[33] Stochastic averaging for the non-autonomous mixed stochastic differential equations with locally Lipschitz coefficients
Wang, Ruifang
Xu, Yong
Yue, Hongge
STATISTICS & PROBABILITY LETTERS, 2022, 182
[34] Regularity of the law of solutions to the stochastic heat equation with non-Lipschitz reaction term
Salins, Michael
Tindel, Samy
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2024, 168
[35] SPDEs with non-Lipschitz coefficients and nonhomogeneous boundary conditions
Xiong, Jie
Yang, Xu
BERNOULLI, 2023, 29 (04) : 2987 - 3012
[36] DENSITY DEPENDENT STOCHASTIC NAVIER-STOKES EQUATIONS WITH NON-LIPSCHITZ RANDOM FORCING
Sango, Mamadou
REVIEWS IN MATHEMATICAL PHYSICS, 2010, 22 (06) : 669 - 697
[37] REGULARITY PROPERTY OF SOLUTION TO TWO-PARAMETER STOCHASTIC VOLTERRA EQUATION WITH NON-LIPSCHITZ COEFFICIENTS
Jiang, Guo
Wang, Xiangjun
ACTA MATHEMATICA SCIENTIA, 2013, 33 (03) : 872 - 882
[38] Caratheodory approximations and stability of solutions to non-Lipschitz stochastic fractional differential equations of Ito-Doob type
Abouagwa, Mahmoud
Liu, Jicheng
Li, Ji
APPLIED MATHEMATICS AND COMPUTATION, 2018, 329 : 143 - 153
[39] THE AVERAGING METHOD FOR MULTIVALUED SDES WITH JUMPS AND NON-LIPSCHITZ COEFFICIENTS
Mao, Wei
Hu, Liangjian
You, Surong
Mao, Xuerong
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (09): : 4937 - 4954
[40] HOMOGENIZATION OF STOCHASTIC SEMILINEAR PARABOLIC EQUATIONS WITH NON-LIPSCHITZ FORCINGS IN DOMAINS WITH FINE GRAINED BOUNDARIES
Sango, Mamadou
COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2014, 12 (02) : 345 - 382

← 1 2 3 4 5 →