Development of stochastic analysis on spaces with anomalous structures

在本研究项目中，我们开发了与随机分析相关的理论，这些理论适合于研究具有异常结构的空间，并考虑到应用。特别是，我们得到了一些新的结果的概念的维数，度量，和局部结构的扩散过程的分形空间。解决了关于新古典不等式的猜想，证明了无穷维状态空间上函数空间的若干性质。

In this research project, we developed theories related to stochastic analysis that were suitable for the study of spaces with anomalous structures, taking applications into consideration. In particular, we obtained some new results on the concepts of dimensions, metrics, and local structures of spaces derived by diffusion processes on fractals. Moreover, we solved the conjecture on the neo-classical inequality, and proved several properties on function spaces on infinite-dimensional state spaces.