Some recent progress in singular stochastic partial differential equations
Some recent progress in singular stochastic partial differential equations
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DOI：
10.1090/bull/1670
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发表时间：
2019-09
影响因子：
1.3
通讯作者：
Ivan Corwin;Hao Shen
中科院分区：
文献类型：
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作者：
Ivan Corwin;Hao Shen
.随机偏微分方程在数学建模中是普遍存在的。然而，许多这样的方程太奇异，不允许经典处理。在这篇文章中，我们回顾了最近的一些进展，在定义，近似，和研究的性质的几个例子，这样的方程。我们主要讨论动力学Φ 4方程、KPZ方程、抛物型安德森模型以及其他一些主要出现在物理学中的方程。当温度接近绝对零度时，它们同样地减小。热涨落是系统温度的基本表现形式。
. Stochastic partial differential equations are ubiquitous in mathematical modeling. Yet, many such equations are too singular to admit classical treatment. In this article we review some recent progress in defining, approxi-mating, and studying the properties of a few examples of such equations. We focus mainly on the dynamical Φ 4 equation, the KPZ equation, and the parabolic Anderson model, as well as a few other equations which arise mainly in physics. in- creases, and likewise they decrease as temperature approaches absolute zero. Thermal fluctuations are a basic manifestation of the temperature of systems.