Abstract
Canonical form, self-decomposability, and the Esscher transforms of Meixner processes are discussed. Mixed Meixner processes are defined and characterized as Markov processes or semimartingales. Ornstein-Uhlenbeck and selfsimilar processes of Meixner type are also described.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. K. Bar-Lev, D. Bshouty, and G. Letac, Natural exponential families and selfdecomposability,Statistics Probab. Lett.,13, 147–152 (1992).
O. E. Barndorff-Nielsen, Normal inverse Gaussian distributions and stochastic volatility modelling,Scand. J. Statist.,24, 1–13 (1996).
O. E. Barndorff-Nielsen, Processes of normal inverse Gaussian type,Finance and Stochastics,2, 41–68 (1998).
O. E. Barndorff-Nielsen, J. L. Jensen, and M. Sørensen, Parametric modelling of turbulence,Philos. Trans. Roy. Soc. London,A332, 439–455 (1990).
O. E. Barndorff-Nielsen, J. L. Jensen, and M. Sørensen,Some stationary processes in discrete and continuous time, Research Report 241, Dept. Theor. Statistics, Aarhus University (1995).
E. Eberlein and U. Keller, Hyperbolic distributions in finance,Bernoulli,1, 281–299 (1995).
H. Gerber and E. Shiu, Option pricing by Esscher-transforms,Trans. Soc. Actuaries,46, (1995).
I. S. Gradshtenyn and I. W. Ryzhik,Table of Integrals, Series and Products, Academic Press, New York (1965).
B. Grigelionis, On mixed exponential processes and martingales,Lith. Math. J.,38(1), 59–74 (1998).
E. Janke, F. Emde, and F. Lösch,Tafeln Höherer Funktionen, Teubner, Stuttgart (1960).
U. Küchler and M. Sørensen,Exponential Families of Stochastic Processes, Springer, Berlin (1997).
G. Letac,Lectures on Natural Exponentials Families and Their Variance Functions, Monografias de Matematica,50, IMPA, Rio de Janeiro (1992).
E. Lukacs,Characteristic Functions, 2nd edn., Charles Griffin, London (1970).
D. B. Madan and F. Milne, Option pricing with V.G. martingale components,Mathematical Finance,1(4), 39–55 (1991).
D. B. Madan and E. Seneta, The Variance Gamma (V.G.) model for share market returns,J. Business,63, 511–524 (1990).
T. H. Rydberg,Generalized hyperbolic diffusions with applications toward finance, Research Report 342, Dept. Theor. Statistics, Aarhus University (1996).
T. H. Rydberg, The normal inverse Gaussian Lévy processes: simulation and approximation,Stochastic Models,13(4), (1996).
K. Sato, Self-similar processes with independent increments,Probab. Theory Related Fields,89, 285–300 (1991).
W. Schoutens and J. L. Teugels, Lévy processes, polynomials and martingales,Commun. Statist.-Stochastic Models,14(1, 2) 335–349 (1998).
Additional information
Partially supported by the Lithuanian State Science and Studies Foundation.
Institute of Mathematics and Informatics, Akademijos 4; Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 39, No. 1, pp. 40–51, January–March, 1999.
Rights and permissions
About this article
Cite this article
Grigelionis, B. Processes of Meixner type. Lith Math J 39, 33–41 (1999). https://doi.org/10.1007/BF02465533
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02465533