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Asymptotic shape of the concave majorant of a Lévy process

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FD2W03 - Optimal control and fractional dynamics

We establish distributional limit theorems for the shape statistics of a concave majorant (i.e. the fluctuations of its length, its supremum, the time it is attained and its value at T) of a Lévy process on [0,T] as T tends to infinity. The scale of the fluctuations of the length and other statistics, as well as their asymptotic dependence, vary significantly with the tail behaviour of the Lévy measure. The key tool in the proofs is the recent representation of the concave majorant for all Lévy processes using a stick-breaking representation.

This talk is part of the Isaac Newton Institute Seminar Series series.

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