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\(\varepsilon\)-strong simulation of the convex minorants of stable processes and meanders. (English) Zbl 1459.60083

Summary: 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 symmetric Lévy processes. We apply this characterisation to construct \(\varepsilon\)-strong simulation \((\varepsilon\) SS) algorithms for the convex minorant of stable meanders, the finite dimensional distributions of stable meanders and the convex minorants of weakly stable processes. We prove that the running times of our \(\varepsilon\) SS algorithms have finite exponential moments. We implement the algorithms in Julia 1.0 (available on GitHub) and present numerical examples supporting our convergence results.

MSC:

60G17 Sample path properties
60G51 Processes with independent increments; Lévy processes
65C05 Monte Carlo methods

Software:

GitHub; SupStable.jl
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References:

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