由时空白噪声驱动的随机反应扩散方程不变测度的运输成本不等式
Transportation-cost inequalities for invariant measures of stochastic reaction-diffusion equations driven by space-time white noise
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中文总结 AI 辅助
研究由乘性时空白噪声驱动的随机反应扩散方程不变测度的运输成本不等式，通过获取随机卷积矩估计，建立随机控制方程解的利普希茨连续性，最终证明了不同度量下的运输成本不等式。
中文摘要 AI 辅助
本文建立了由乘性时空白噪声驱动的随机反应扩散方程不变测度的运输成本不等式。具体而言，在漂移项不同耗散强度下，针对\(L^1\)度量、\(L^2\)度量和一致度量建立了运输成本不等式。首先得到了由时空白噪声驱动的随机卷积的全局时间和空间一致矩估计，然后建立了相关随机控制方程解关于控制量的具有与时间无关的利普希茨常数的利普希茨连续性，最后证明了随机反应扩散方程不变测度的运输成本不等式。
英文摘要
In this paper, we establish transportation-cost inequalities for invariant measures of stochastic reaction-diffusion equations driven by multiplicative space-time white noise. In particular, the transportation-cost inequalities are established with respect to the $L^1$ metric, the $L^2$ metric and the uniform metric under different dissipativity strengths of the drift. We first obtain a global-in-time and spatially uniform moment estimate for stochastic convolutions driven by space-time white noise, which is of independent interest. We then establish Lipschitz continuity of the solutions to the associated stochastic controlled equations with respect to the controls with a time-independent Lipschitz constant. Applying this Lipschitz continuity estimate, we finally prove transportation-cost inequalities for the invariant measures of stochastic reaction-diffusion equations.
