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

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.

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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

Information

Received: 1 March 2014; Revised: 1 October 2017; Published: November 2018
First available in Project Euclid: 25 September 2018

zbMATH: 06975484
MathSciNet: MR3857853
Digital Object Identifier: 10.1214/17-AOP1239

Subjects:
Primary: 60H10
Secondary: 60H40, 60J80

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 6 • November 2018
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