报告人：范爱华 教授（法国Picardie大学/武汉大学）

时间：2026年05月18日 09:30-

地点：理科楼LA104

摘要：Classical fractal and multifractal theories mostly study objects in finite-dimensional spaces. How should we deal with objects in infinite-dimensional spaces? The distribution of Brownian motion is a Borel probability measure supported on the infinite-dimensional space C([0,1]), which is not translation-invariant but only partially quasi-invariant under translation. Its local behavior exhibits multifractal characteristics. It is the nature of Brownian motion. We can adopt a more general concept of "scale" instead of dimension, and conduct quantitative studies leveraging a comprehensive understanding of Brownian motion. The distribution measures of stochastic processes remain largely unexplored, especially Gaussian measures on Banach spaces, such as the distribution of solution processes to stochastic differential equations driven by Brownian motion. We will present the basic theoretical framework and the viable methods for Gaussian measures on Hilbert spaces.

邀请人：数学研究中心

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