PATHWISE UNIQUENESS OF THE STOCHASTIC HEAT EQUATION WITH SPATIALLY INHOMOGENEOUS WHITE NOISE

• 成果类型: Article
• 署名作者: Neuman, Eyal
• 署名单位: Imperial College London
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1239
• 发表日期: 2018
• 页码: 3090-3187
• 关键词: partial-differential-equations; nonuniqueness; coefficients

摘要

We study the solutions of the stochastic heat equation driven by spatially inhomogeneous multiplicative white noise based on a fractal measure. We prove pathwise uniqueness for solutions of this equation when the noise co-efficient is Holder continuous of index gamma > 1 - eta/2(eta+1). Here eta is an element of (0, 1) is a constant that defines the spatial regularity of the noise.