Transportation inequalities under uniform metric for a stochastic heat equation driven by time-white and space-colored noise

Shijie shang; Ran Wang

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arXiv · 1910.04934

Transportation inequalities under uniform metric for a stochastic heat equation driven by time-white and space-colored noise

Shijie shang·Ran Wang

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Abstract

In this paper, we prove transportation inequalities on the space of continuous paths with respect to the uniform metric, for the law of solution to a stochastic heat equation defined on $[0,T]\times [0,1]^d$. This equation is driven by the Gaussian noise, white in time and colored in space. The proof is based on a new moment inequality under the uniform metric for the stochastic convolution with respect to the time-white and space-colored noise, which is of independent interest.

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Shijie shang, Ran Wang. 2019-10-11. Transportation inequalities under uniform metric for a stochastic heat equation driven by time-white and space-colored noise. https://arxiv.org/abs/1910.04934

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