Central Limit Theorems

Central limit theorems have played a paramount role in probability theory starting—in the case of independent random variables—with the DeMoivre- Laplace version and culminating with that of Lindeberg—Feller. The term “central” refers to the pervasive, although nonunique, role of the normal distribution as a limit of d.f.s of normalized sums of (classically independent) random variables. Central limit theorems also govern various classes of dependent random variables and the cases of martingales and interchangeable random variables will be considered.