Wiener–Hopf factorization and distribution of extrema for a family of Lévy processes
Wiener–Hopf factorization and distribution of extrema for a family of Lévy processes
In this paper we introduce a ten-parameter family of Lévy processes for which we obtain Wiener-Hopf factors and distribution of the supremum process in semi-explicit form. This family allows an arbitrary behavior of small jumps and includes processes similar to the generalized tempered stable, KoBoL and CGMY processes. Analytically it …