Stochastic Partial Differential Equations:Kolmogorov Operators and Invariant Measures

Wilhelm Stannat

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Stochastic Partial Differential Equations:Kolmogorov Operators and Invariant Measures

机译：随机偏微分方程：Kolmogorov算子和不变测度

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Stochastic partial differential equations are an important tool in the modelling and analysis of complex random dynamical systems. We present a survey on the semigroup approach to their solution and on the main concepts applied today to analyze them. In particular, we review recent results obtained on the existence of invariant measures, (improved) moment estimates and their support properties, as well as uniqueness results for associated Kolmogorov operators. The survey is complemented with various illustrations and a discussion of those examples that have been essential for the development of the theory.

机译：随机偏微分方程是复杂随机动力系统建模和分析的重要工具。我们对半组方法及其解决方案以及当今用于分析它们的主要概念进行了调查。特别是，我们回顾了有关不变测度，（改进的）矩估计及其支持特性以及相关Kolmogorov算子的唯一性结果的存在而获得的最新结果。该调查辅以各种插图，并对这些实例的发展进行了讨论，这些实例对于理论的发展至关重要。

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来源
《Jahresbericht der Deutschen Mathematiker-Vereinigung》 |2011年第2期|p.81-109|共29页
作者
Wilhelm Stannat;
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作者单位

Fachbereich Mathematik, Technische Universitat Darmstadt, SchloBgartenstraGe 7,64289 Darmstadt, Germany;

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正文语种 eng
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关键词
stochastic partial differential equations; mild solutions; kolmogorov operators; invariant measures; moment estimates; krylov-bogoliubov theory; l~p -uniqueness;

机译：随机偏微分方程;温和溶液;kolmogorov算子;不变测度;力矩估计;克雷洛夫-波哥留波夫理论l〜p-唯一性;

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专利

1. Stochastic Partial Differential Equations: Kolmogorov Operators and Invariant Measures [J] . Wilhelm Stannat Jahresbericht der Deutschen Mathematiker-Vereinigung . 2011,第2期

机译：随机偏微分方程：Kolmogorov算子和不变测度
2. A full-discrete exponential Euler approximation of the invariant measure for parabolic stochastic partial differential equations [J] . Ziheng Chen, Siqing Gan, Xiaojie Wang Applied numerical mathematics . 2020,第Nova期

机译：抛物面随机偏微分方程不变度量的全离散指数欧拉近似
3. Existence of Invariant Measures for Reflected Stochastic Partial Differential Equations [J] . Journal of theoretical probability . 2020,第3期

机译：反射随机偏微分方程不变措施的存在
4. Linear Operators and Stochastic Partial Differential Equations in Gaussian Process Regression [C] . Simo Saerkkae International conference on artificial neural networks;ICANN 2011 . 2011

机译：高斯过程回归中的线性算子和随机偏微分方程
5. Numerical Approximation of Partial Differential Equations Involving Fractional Differential Operators [D] . Lei, Wenyu 2018

机译：包含分数阶微分算子的偏微分方程的数值逼近
6. Differential Invariants and Invariant Partial Differential Equations Under Continuous Transformation Groups in Normed Linear Spaces [O] . Aristotle D. Michal 1951

机译：赋范线性空间中连续变换群下的微分不变量和不变性偏微分方程
7. On a class of stochastic partial differential equations with multiple invariant measures [O] . Bálint Farkas, Martin Friesen, Barbara Rüdiger, 2021

机译：在具有多种不变措施的一类随机偏微分方程
8. Nonlinear Partial Differential Equations and Invariant Differential Systems [R] . Estabrook, F. B., Wahlquist, H. D. 1987

机译：非线性偏微分方程与不变微分系统

Stochastic Partial Differential Equations:Kolmogorov Operators and Invariant Measures

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