Speaker: Prof. FAN Aihua，Picardie University, France

Title: Fractal Analysis of Gaussian Measures in Infinite-dimensional Banach Spaces

Language: English

Time & Venue: 2026.05.22 16:00-17:00 南楼N620

Abstract: Classical fractal and multifractal theory studied objects (from analysis, probability, dynamical systems) in finite-dimensional spaces. How could we deal with objects in infinite-dimensional spaces? A typical example is the Wiener measure, a Borel probability measure supported on the infinite-dimensional space C([0,1]) of continuous functions, which is not translation-invariant but only partially quasi-invariant under translation (Cameron-Martin theorem). Its local behavior exhibits multifractal feature. We can adopt a more general concept of "scale" instead of “dimension”, and conduct quantitative studies leveraging a comprehensive understanding of the Wiener measure. But, the probability laws of stochastic processes, gaussian or non-gaussian, remain largely unexplored, especially Gaussian measures on Banach spaces. For the time being, we can only deal with Gaussian measures on Hilbert spaces. The results about the Wiener measure is a joint work with Mathieu Helfter. In this talk, we will also present basic frameworks and open questions.