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.
Citation
Eyal Neuman. "Pathwise uniqueness of the stochastic heat equation with spatially inhomogeneous white noise." Ann. Probab. 46 (6) 3090 - 3187, November 2018. https://doi.org/10.1214/17-AOP1239
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