= Fabrice Baudoin
{c}
<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.https://pure.au.dk/portal/en/persons/fbaudoin%40math.au.dk/[Institutional research statement]{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.<Itō's representation theorem by Fabrice Baudoin>[Theorem and corollary; completed natural Brownian filtration]{ref}
\Image[https://pure.au.dk/portal/files-asset/362206689/portrait-4low.JPG?f=jpg&w=160]
{title=Fabrice Baudoin}
{description=Portrait identified by the author's Aarhus University profile.}
{source=https://pure.au.dk/portal/en/persons/fbaudoin%40math.au.dk/}
{width=160}
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