Levy过程驱动的随机偏微分方程是随机分析的基本内容，因其可以描述现实中不连续现象的独特优势，在金融数学等许多领域有广泛应用。作为一类基本的非连续过程，Levy过程与布朗运动有着本质的区别；Levy过程驱动的随机偏微分方程方面的研究需要理论和方法上的创新。本项目将分为两部分从理论分析角度进行研究：（1）随机过程的时间正则性（即其轨道关于时间为右连续左极限存在）是研究随机过程强马氏性、可测性、Doob停时定理等精细性质的基础。本项目的目的之一是研究Levy过程驱动的随机偏微分方程的时间正则性。（2）大偏差理论主要研究罕见事件事发概率为指数型的估计，在统计力学，统计，金融等众多领域都有重要和深刻的应用。本项目另一个目的是研究乘法Levy过程驱动的随机偏微分方程大偏差理论，特别地研究乘法Levy过程驱动的随机发展方程和二维随机Navier-Stokes方程的大偏差。

Stochastic partial differential equations(SPDEs) driven by Levy noise is one of the essential contents of stochastic analysis, and owing to its special advantage in characterizing discontinuous phenomena, it is widely used in Mathematical Finance and many other research fields. As a fundamental class of discontinuous processes, Levy process has essential difference with Brown motion; the research on SPDEs driven by Levy noise requires theoretical and methodological innovations. This project will focus on theoretical analysis on SPDEs driven by Levy noise, and will be divided into two parts. First, the time regularity of stochastic process plays an important role in the study of some finer structural properties, such as strong Markov property, measurability and Doob's stopping time theorem. Our first aim is to study the time regularity of SPDEs driven by Levy noise. Second, large deviation principle mainly studies the probabilities of rare events that are exponentially small, and has important and deep applications in many research fields, such as Statistical Mechanics, Statistics and Finance. Our second aim is to study large deviation principle for SPDEs driven by multiplicative Levy noise. Particularly we will study large deviation principle for stochastic evolution equations and two-dimensional stochastic Navier-Stokes equations, both driven by multiplicative Levy noise.