The study of stochastic areas was initiated by Paul Lévy in his 1950 seminal paper in which he derived the characteristic function of the area swept out by the path up to time t>0 of a planar Brownian motion started at the origin. Over the last few years, this research direction has seen renewed interest, which has led, in particular, to the publication of Stochastic Areas, Horizontal Brownian motions, and Hypoelliptic Heat Kernels by Baudoin, Demni and Wang. As the complex plane appearing in Lévy's paper is the model for irreducible simply connected Hermitian symmetric spaces of flat type, one can wonder how his results transpose to the compact and non-compact types. In this talk we present a Jordan theoretic approach addressing all non-flat cases at once and derive the characteristic function as well as the asymptotic behaviour of the stochastic area process.
