The Annals of Probability

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

Eyal Neuman

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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

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

Received: March 2014
Revised: October 2017
First available in Project Euclid: 25 September 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60H40: White noise theory 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Uniqueness white noise stochastic partial differential equations heat equation catalytic superprocesses


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.

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