渐近强费勒与弱可观测性不等式
Asymptotic strong Feller and weak observability inequality
浏览论文内容
中文总结 AI 辅助
研究一类非自治线性随机偏微分方程，通过结合偏微分方程控制理论与马利瓦因微积分，建立渐近正则化等之间的等价关系及半线性方程准则，并应用于随机奥森等方程。
中文摘要 AI 辅助
对于一类非自治线性随机偏微分方程，我们建立了相关确定性控制系统的渐近正则化、弱可观测性和近似零能控性之间的等价关系。这种等价关系为随机平滑提供了确定性控制理论特征，并为研究由空间局部噪声驱动的随机偏微分方程提供了系统方法。我们还基于线性化方程的弱可观测性为半线性随机偏微分方程建立了一个准则。我们的方法将偏微分方程控制理论方法与马利瓦因微积分相结合。作为应用，我们考虑了由有限维、空间局部白噪声驱动的随机奥森方程、非自治一致抛物方程和抛物型正弦 - 戈登方程。
英文摘要
For a class of non-autonomous linear SPDEs, we establish the equivalence among asymptotic regularization, weak observability, and approximate null controllability for the associated deterministic control systems. This equivalence provides a deterministic control-theoretic characterization of stochastic smoothing and offers a systematic approach to studying SPDEs driven by spatially localized noise. We further establish a criterion for semilinear SPDEs based on weak observability of the linearized equations. Our approach combines methods from PDE control theory with Malliavin calculus. As applications, we consider the stochastic Oseen equation, non-autonomous uniformly parabolic equations, and the parabolic Sine--Gordon equation, all driven by finite-dimensional, spatially localized white-in-time noise.
