Stochastic Partial Differential Equations and Interacting particle systems

从广义上讲，就我博士学位的主题而言，它涉及分析，随机分析和变分法的相互作用。准确地说，该项目将主要集中在随机偏微分方程（SPDE）的主题上。随机偏微分方程是一个较新的领域，其研究的必要性已被应用所激发。例如，在物理学中，从随机介质中的波传播和湍流等问题。生物学和神经生物学，特别是群体遗传学，也给了我很大的启发。2014年，在随机偏微分方程领域取得了重大发现，这为我们研究新问题提供了广阔的前景。随机偏微分方程的分析也与相互作用的粒子系统有关，我的博士学位就在这两个领域之间。在我的博士学位，我们将研究非线性随机偏微分方程和相关的相互作用的粒子系统，我们将看到这两个学科如何走到一起来描述解决方案的长期行为。

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.