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 ...

Some general results concerning the asymptotic behavior of the value of the empirical distribution function at a random point (e.g. the sample mean) are given. These results are then used to obtain: ...

Understanding the mechanisms responsible for stability and persistence of ecosystems is one of the greatest challenges in ecology. Robert May showed that, contrary to intuition, complex randomly built ...

Goodness-of-fit testing forms a fundamental pillar in statistical methodology, providing robust tools to assess whether observed data conform to a proposed probability distribution. These tests are ...