The Annals of Probability

Pathwise uniqueness of the stochastic heat equation 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 $\gamma>1-\frac{\eta}{2(\eta+1)}$. 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
Received: March 2014
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

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

Keywords
Uniqueness white noise stochastic partial differential equations heat equation catalytic superprocesses

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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