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Session Overview |
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S 2 Keynote: Spatial stochastics, disordered media, and complex networks
Session Topics: 2. Spatial stochastics, disordered media, and complex networks
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1:40 pm - 2:30 pm
Multiple Poisson Integrals: from U-statistics to Poincaré inequalities Multiple Wiener-Itô integrals with respect to Poisson measures are fundamental tools in modern stochastic analysis. Despite their widespread use, they remain less understood than their Gaussian counterparts, with key questions about their regularity—such as the existence of higher moments or hypercontractivity properties—still open for investigation. In this talk, I will first explore the applications of multiple integrals in a stochastic geometric context, particularly through the lens of U-statistics. I will then turn to product formulae, and show how a recent extension of the classical Poincaré inequality has enabled us to derive comprehensive necessary and sufficient conditions for the validity of product formulae of arbitrary length. This result substantially resolves a longstanding open question from one of Surgailis's seminal papers (1984). The second part of the talk is based on joint work with Lorenzo Cristofaro (Luxembourg). | ||
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