A note on central limit theorems for quadratic variation in case of   endogenous observation times
  This paper is concerned with a central limit theorem for quadratic variation when observations come as exit times from a regular grid. We discuss the special case of a semimartingale with deterministic characteristics and finite activity jumps in detail and illustrate technical issues in more general situations. 
Mathias Vetter, Tobias Zwingmann
math.ST stat.TH