250318 VO Selected topics in probability theory (2008S)

This course is devoted to questions of distributional convergence. If we interpret the partial sums of a sequence of random variables (independent, identically distributed, and bounded, say) as the positions of a random walk, the central limit theorem describes the asymptotic distribution of the latter. Significantly more information is given by "functional" limit theorems which provide corresponding statements about the whole process. A more detailed preview will be given in the first lecture.