拟正则狄氏型理论是由马志明院士等人建立起来的现代数学理论，该理论及其应用至今仍是现代随机分析领域的一个重要研究方向。本项目包括三方面内容：（1）将对称狄氏过程的随机积分扩展到非对称狄氏过程及半狄氏过程的情形。并把它应用于非对称马氏过程的Feynman-Kac变换、Girsanov变换、非对称（半）狄氏型的广义Fukushima分解、具有奇异系数的Dirichlet边值问题等问题的研究；（2）研究非对称狄氏型的光滑测度与可加泛函之间的关系，特别是同一个光滑测度关于一对对偶过程可加泛函之间的关系。期望能刻画非对称狄氏型kato-类光滑测度的特征，进一步研究狄氏过程的可加泛函在测度变化下的性质；（3）关于狄氏过程大偏差问题的研究，特别是零能量连续可加泛函的大偏差问题。我们期望将对称情形的结果推广到非对称情形，并将它应用于半群L^p独立性的研究。这三个问题的解决将进一步完善狄氏型理论及大偏差理论。

The quasi-regular Dirichlet form theory is a modern mathematical theroy that was developed by Zhiming Ma and others. This theory builds up a bridge between classical analysis and probability. Presently, the theory and its applications are one of important branches in stochastic analysis. This project consists of three parts. In the first part, we will generalize stochastic integrals from symmetric Dirichlet processes to non-symmetric Dirichlet processes and semi-Dirichlet processes. The stochastic integrals will be applied to study Feynman-Kac transformations and Girsanov transformations of non-symmetric Markov processes，and will also be applied to study Fukushima's decomposition of non-symmetric (semi-) Dirichlet forms and Dirichlet boundary value problems of singular coefficients. In the second part, we will investigate the relationship between smooth measures and additive functionals of non-symmetric Dirichlet processes. For a smooth measure and a pair of dual processes, we will focus on the relationship of two additive functionals whose Revuz measures are the given smooth measure. We expect to characterize the Kato class of smooth measures in the non-symmetric Dirichlet forms case. We will also study the properties of additive functionals under measure transformations. In the third part, we will study large deviation of Dirichlet processes. We wish to first extend the results of symmetric Dirichlet processes to the non-symmetric case, and then apply these results to the research of the L^p independence of semi-groups. The resolvements of the above three problems will further perfect Dirichlet forms theory and large deviation theory.