Stochastic Calculus for symmetric diffusion processes and its applications

首席研究员成功地将对称扩散的随机微积分应用于不同国家的研究人员的不同主题，结果已发表在三个国际期刊上。首席研究员与研究人员合作开发具有压缩p-范数的一般函数空间的势理论，并将其应用于d-集和相关跳跃型马尔可夫过程的Besov空间的研究。对一般对称马氏过程，证明了测度的容性等周不等式等价于测度支撑下的时变过程的超压缩性.研究结果作为三篇论文发表在国际期刊上。

The head investigator has succeeded to apply the stochastic calculus of symmetric diffusions to different subjects with researchers in different countries, and the results have been published in three international journals. The head investigator collaborates with investigators to develop potential theory for a general function space with contractive p-norm and apply it to the study of Besov spaces on d-sets and associated jump type Markov processes. Furthermore, for a general symmetric Markov process, a capacitary isoperimetric inequality of a measure is shown to be equivalent to the ultracontractivity of the time changed process on the support of measure. The results are being published as three papers in international journals.