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How smooth can the convex hull of a Lévy path be?
David Bang, Jorge González Cázares, Aleksandar Mijatović
We describe the rate of growth of the derivative of the convex minorant of a Lévy path at times where increases continuously. Since the convex minorant is piecewise linea…
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…
-strong simulation of the convex minorants of stable processes and meanders
Jorge Ignacio González Cázares, Aleksandar Mijatović, Gerónimo Uribe Bravo
Using marked Dirichlet processes we characterise the law of the convex minorant of the meander for a certain class of Lévy processes, which includes subordinated stable and symmetr…
Exact Simulation of the Extrema of Stable Processes
Jorge Ignacio González Cázares, Aleksandar Mijatović, Gerónimo Uribe Bravo
We exhibit an exact simulation algorithm for the supremum of a stable process over a finite time interval using dominated coupling from the past (DCFTP). We establish a novel perpe…