Open Access
Translator Disclaimer
2014 Integral and local limit theorems for level crossings of diffusions and the Skorohod problem
Rafał Łochowski, Raouf Ghomrasni
Author Affiliations +
Electron. J. Probab. 19: 1-33 (2014). DOI: 10.1214/EJP.v19-2644

Abstract

Using a new technique, based on the regularisation of a càdlàg process via the double Skorohod map, we 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. We also extend to diffusions the classical result of Kasahara on the "local" limit theorem for the number of crossings of a Wiener process. We establish the correspondence between the truncated variation and the double Skorohod map. Additionally, we prove some auxiliary formulas for the Skorohod map with time-dependent boundaries.

Citation

Download Citation

Rafał Łochowski. Raouf Ghomrasni. "Integral and local limit theorems for level crossings of diffusions and the Skorohod problem." Electron. J. Probab. 19 1 - 33, 2014. https://doi.org/10.1214/EJP.v19-2644

Information

Accepted: 17 January 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1296.60082
MathSciNet: MR3164763
Digital Object Identifier: 10.1214/EJP.v19-2644

Subjects:
Primary: 60F17
Secondary: 60F15 , 60G17 , 60G44

Keywords: Diffusions , interval crossings , level crossings , Local time , Semimartingales , the Skorohod problem , truncated variation

JOURNAL ARTICLE
33 PAGES


SHARE
Vol.19 • 2014
Back to Top