Non-uniqueness of the first passage time density of Lévy random processes. (English) Zbl 1071.60033
The authors consider a class of random processes they call Lévy processes, with long-tailed jump lengths, but which are not simple jump processes as functions of a clock time. They derive the first passage time density (FPTD) for such processes from a subordination scheme to either a Lévy flight or a Brownian random walk. It appears that this FPTD cannot be inferred uniquely from the probability density functions governing the random processes considered.
Reviewer: Marius Iosifescu (Bucureşti)
MSC:
60G51 | Processes with independent increments; Lévy processes |
60J25 | Continuous-time Markov processes on general state spaces |