We derive limit theorems for the empirical distribution function of "devolatilized" increments of an Ito semimartingale observed at high frequencies. These "devolatilized" increments are formed by ...

We study geometric moment contracting properties of nonlinear time series that are expressed in terms of iterated random functions. Under a Dini-continuity condition, a central limit theorem for ...

Universality theorems occupy a central role in analytic number theory, demonstrating that families of analytic functions—including the prototypical Riemann zeta-function—can approximate an extensive ...

Hypergeometric functions are at the heart of many analytical and applied mathematical investigations. These functions, generally defined via power series that extend the geometric series, have been ...

In the Idea of Limits video, we introduce the idea of limits and discuss how it underpins all of the major concepts in calculus. In the Limit Laws video, we introduce the limit laws and discuss how to ...