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

Prelegent(ci)

Rafał Łochowski

Afiliacja

Szkoła Główna Handlowa

Termin

4 kwietnia 2013 12:15

Pokój

p. 3260

Seminarium

Seminarium Zakładu Rachunku Prawdopodobieństwa

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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.

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