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[null,"1.","Record Nr.",null,"UNINA9910557372503321"]
[null,null,"Autore",null,"Avram Florin"]
[null,null,"Titolo",null,"Exit  Problems  for  Lévy and Markov Processes with  One-Sided Jumps and Related Topics"]
[null,null,"Pubbl/distr/stampa",null,"Basel, Switzerland, : MDPI - Multidisciplinary Digital Publishing Institute, 2021"]
[null,null,"Descrizione fisica",null,"1 online resource (218 p.)"]
[null,null,"Soggetti",null,"Mathematics and Science"]
[{"$nulls":4},"Research and information: general"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Sommario/riassunto","Exit problems for one-dimensional Lévy processes are easier when jumps only occur in one direction. In the last few years, this intuition became more precise: we know now that a wide variety of identities for exit problems of spectrally-negative Lévy processes may be ergonomically expressed in terms of two q-harmonic functions (or scale functions or positive martingales) W and Z. The proofs typically require not much more than the strong Markov property, which hold, in principle, for the wider class of spectrally-negative strong Markov processes. This has been established already in particular cases, such as random walks, Markov additive processes, Lévy processes with omega-state-dependent killing, and certain Lévy processes with state dependent drift, and seems to be true for general strong Markov processes, subject to technical conditions. However, computing the functions W and Z is still an open problem outside the Lévy and diffusion classes, even for the simplest risk models with state-dependent parameters (say, Ornstein-Uhlenbeck or Feller branching diffusion with phase-type jumps)."]