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arXiv · 1403.4491

Pathwise Uniqueness of the Stochastic Heat Equations with Spatially Inhomogeneous White Noise

Eyal Neuman
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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 $γ>1-\fracη{2(η+1)}$. Here $η\in(0,1)$ is a constant that defines the spatial regularity of the noise.

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Eyal Neuman. 2014-03-18. Pathwise Uniqueness of the Stochastic Heat Equations with Spatially Inhomogeneous White Noise. https://arxiv.org/abs/1403.4491

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