Julia package SupStable.jl: Exact simulation of the extrema of stable processes. 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 perpetuity equation for the supremum (via the representation of the concave majorants of Lévy processes ) and use it to construct a Markov chain in the DCFTP algorithm. We prove that the number of steps taken backwards in time before the coalescence is detected is finite. We analyse the performance of the algorithm numerically (the code, written in Julia 1.0, is available on GitHub)
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References in zbMATH (referenced in 3 articles , 1 standard article )
Showing results 1 to 3 of 3.
- Cázares, Jorge I. González; Mijatović, Aleksandar; Bravo, Gerónimo Uribe: (\varepsilon)-strong simulation of the convex minorants of stable processes and meanders (2020)
- Hernández, Osvaldo Angtuncio; Bravo, Gerónimo Uribe: Dini derivatives and regularity for exchangeable increment processes (2020)
- Cázares, Jorge I. González; Mijatović, Aleksandar; Bravo, Gerónimo Uribe: Exact simulation of the extrema of stable processes (2019)