Stochastic Partial Differential Equations and Interacting particle systems

概括地说，就我的博士课程而言，它涉及分析、随机分析和变分计算的相互作用。准确地说，这个项目将主要集中在随机偏微分方程组(SPDEs)的主题上。随机偏微分方程组是一个比较新的领域，研究随机偏微分方程组的必要性已经受到了应用的强烈推动。例如，在物理学中，来自随机介质中的波传播和湍流等问题。重要的刺激也来自生物学和神经生物学，特别是来自种群遗传学。最近在2014年进行的研究工作导致了随机偏微分方程领域的重大发现，这为需要研究的广泛新问题打开了大门。随机偏微分方程的分析也与相互作用的粒子系统有关，我的博士学位介于这两个领域之间。在我的博士学位期间，我们将研究非线性随机偏微分方程组和相关的相互作用的粒子系统，我们将看到这两个学科是如何结合在一起来描述解的长期行为的。

In broad terms, as far as the subject of my PhD is concerned, it involves an interplay of analysis, stochastic analysis and calculus of variations.To be precise, the project will be mainly focused on the topic of Stochastic Partial Differential Equations (SPDEs). Field of Stochastic Partial Differential Equations is quite new, the necessity of studying Stochastic Partial Differential Equations has been strongly motivated by applications. For example, in physics from problems such as wave propagation in random media and turbulence. Significant stimuli have also come from biology and neurobiology, in particular from population genetics.Recent research efforts conducted in 2014 led to major discoveries in the field of Stochastic Partial Differential Equations, and this has opened to a wide range of new problems to be studied.The analysis of Stochastic Partial Differential Equations is also related to interacting particle systems and my PhD is between these two areas. Throughout my PhD we will look into non-linear Stochastic Partial Differential Equations and related interacting particle systems and we will see how these two disciplines come together to describe the long-time behavior of the solution.