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
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
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