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4 papers · 2 filters
Asymptotic shape of the concave majorant of a Lévy process
David Bang, Jorge Ignacio González Cázares, Aleksandar Mijatović
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…
Convex minorants and the fluctuation theory of Lévy processes
Jorge Ignacio González Cázares, Aleksandar Mijatović
We establish a novel characterisation of the law of the convex minorant of any Lévy process. Our self-contained elementary proof is based on the analysis of piecewise linear convex…
A Gaussian approximation theorem for Lévy processes
David Bang, Jorge Ignacio González Cázares, Aleksandar Mijatović
Without higher moment assumptions, this note establishes the decay of the Kolmogorov distance in a central limit theorem for Lévy processes. This theorem can be viewed as a continu…
Implementable coupling of Lévy process and Brownian motion
Vladimir Fomichov, Jorge González Cázares, Jevgenijs Ivanovs
We provide a simple algorithm for construction of Brownian paths approximating those of a Lévy process on a finite time interval. It requires knowledge of the Lévy process trajecto…