1 research outputs found
-strong simulation of the convex minorants of stable processes and meanders
Using marked Dirichlet processes we characterise the law of the convex
minorant of the meander for a certain class of L\'evy processes, which includes
subordinated stable and symmetric L\'evy processes. We apply this
characterisaiton to construct -strong simulation (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 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.Comment: 38 pages, 8 figure