Fabrice Baudoin

Fabrice Baudoin studies stochastic calculus and differential geometry, using diffusion processes and heat kernels to obtain functional inequalities. His Aarhus University research profile describes this exchange: geometric information can bound a diffusion, while probabilistic methods can reveal properties of the underlying space.^[ref]

His lecture Itō's representation theorem by Fabrice Baudoin illustrates the role of a precise information structure. For the completed natural filtration of Brownian motion, a square-integrable terminal random variable can be written as its expected value plus a stochastic integral. This yields a continuous version of each square-integrable martingale in that filtration. His exposition develops the Brownian martingale representation theorem through its filtration and square-integrability assumptions.^[ref]