随机偏微分方程重正化的微局部方法
A Microlocal Approach to Renormalization in Stochastic PDEs
摘要：
我们提出了一个新的框架来研究一大类非线性随机偏微分方程，这是受量子场论的代数方法的启发。其主要优点是，通过实现随机场内的一个适当的代数的功能值分布，我们能够使用技术适当的微局部分析，使我们能够讨论重整化及其相关的freedomw不诉诸任何正规化计划和减去无穷大。作为一个例子的有效性的方法，我们将其应用到扰动分析的随机$Φ^3_d$模型。
英文摘要：
We present a novel framework for the study of a large class of non-linear stochastic PDEs, which is inspired by the algebraic approach to quantum field theory. The main merit is that, by realizing random fields within a suitable algebra of functional-valued distributions, we are able to use techniques proper of microlocal analysis which allow us to discuss renormalization and its associated freedomw without resorting to any regularization scheme and to the subtraction of infinities. As an example of the effectiveness of the approach we apply it to the perturbative analysis of the stochastic $Φ^3_d$ model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
