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2019 Talagrand concentration inequalities for stochastic heat-type equations under uniform distance
Shijie Shang, Tusheng Zhang
Electron. J. Probab. 24: 1-15 (2019). DOI: 10.1214/19-EJP388

Abstract

In this paper, we established a quadratic transportation cost inequality under the uniform/maximum norm for solutions of stochastic heat equations driven by multiplicative space-time white noise. The proof is based on a new inequality we obtained for the moments of the stochastic convolution with respect to space-time white noise, which is of independent interest. The solutions of such stochastic partial differential equations are typically not semimartingales on the state space.

Citation

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Shijie Shang. Tusheng Zhang. "Talagrand concentration inequalities for stochastic heat-type equations under uniform distance." Electron. J. Probab. 24 1 - 15, 2019. https://doi.org/10.1214/19-EJP388

Information

Received: 1 April 2019; Accepted: 5 November 2019; Published: 2019
First available in Project Euclid: 12 November 2019

zbMATH: 07142923
MathSciNet: MR4040989
Digital Object Identifier: 10.1214/19-EJP388

Subjects:
Primary: 60H15
Secondary: 35R60, 93E20

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Vol.24 • 2019
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