Integral and local limit theorems for level crossings of diffusions and the Skorohod problem

Using a new technique, based on the regularisation of a càdlàg process via the double Skorohod map, I obtain limit theorems for integrated numbers of level crossings of diffusions. This result is related to the recent results on the limit theorems for the truncated variation. I also extend to diffusions the classical result of Kasahara on the "local" limit theorem for the number of crossings of a Wiener process. I establish the correspondence between the truncated variation and the double Skorohod map. The talk is based on the joint paper with Raouf Ghomrasni from the African Institute for Mathematical Sciences.