Based on the first author’s recent PhD thesis entitled “Profiling processes of Meixner type”,  a review of the main characteristics and characterizations of such particular Lévy processes is extracted, emphasizing the motivations for their introduction in literature as reliable financial models. An insight on orthogonal polynomials is also provided, together with an alternative path for defining the same processes. Also, an attempt of simulation of their trajectories is introduced by means of an original R simulation routine.
"Reviewing alternative characterizations of Meixner process." Probab. Surveys 8 127 - 154, 2011. https://doi.org/10.1214/11-PS177