## The Annals of Probability

### Pathwise uniqueness of the stochastic heat equation with spatially inhomogeneous white noise

Eyal Neuman

#### Abstract

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 coefficient is Hölder continuous of index $\gamma>1-\frac{\eta}{2(\eta+1)}$. Here $\eta\in(0,1)$ is a constant that defines the spatial regularity of the noise.

#### Article information

Source
Ann. Probab., Volume 46, Number 6 (2018), 3090-3187.

Dates
Revised: October 2017
First available in Project Euclid: 25 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.aop/1537862429

Digital Object Identifier
doi:10.1214/17-AOP1239

Mathematical Reviews number (MathSciNet)
MR3857853

Zentralblatt MATH identifier
06975484

#### Citation

Neuman, Eyal. Pathwise uniqueness of the stochastic heat equation with spatially inhomogeneous white noise. Ann. Probab. 46 (2018), no. 6, 3090--3187. doi:10.1214/17-AOP1239. https://projecteuclid.org/euclid.aop/1537862429

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