Stochastic Calculus for symmetric diffusion processes and its applications

首席研究员已经成功地将对称扩散的随机演算与不同国家的研究人员一起应用于不同的主题，并且结果已在三个国际期刊上发表。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潜在理论，并将其应用于d集上的Besov空间和相关的跳跃型马尔可夫过程的研究。进一步，对于一般对称马尔可夫过程，证明了测度的容性等周不等式等价于测度支持下时变过程的超收缩性。研究结果以三篇论文的形式发表在国际期刊上。

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.