Regular Lévy Processes of Exponential type in 1D

The following sections are included:Model ClassesAn overviewKoBoL family: direct construction via the Lévy-Khintchine formulaDefinition in terms of the Lévy measureThe characteristic exponentMoments of a KoBoL processGraphs of characteristic exponents and probability densities of different KoBoL processesProofs of technical lemmasNormal Inverse Gaussian processes and Normal Tempered Stable Lévy Processes: construction via subordinationVariance Gamma ProcessesHyperbolic Processes and Generalized Hyperbolic ProcessesComparison of the tail behaviour of probability densities for different model classes of processesTwo definitions of Regular Lévy Processes of Exponential typeDefinition in terms of the Lévy measureDefinition in terms of the characteristic exponentProperties of the characteristic exponents and probability densities of RLPEProperties of the infinitesimal generatorsA “naive approach” to the construction of RLPE or why they are natural from the point of view of the theory of PDOModified Stable Processes and RLPEThe Wiener-Hopf factorizationThe case of Lévy processes of exponential typeThe Wiener-Hopf factorization for RLPEApproximate formulas for the factors in the case of NIG, HP, KoBoL and NTS Lévy processes