Stationary and self-similar processes driven by Lévy processes

Stochastic Processes and their Applications

Volumn 84, Issue 2, 1999, Pages 357-369

  Barndorff Nielsen, Ole E ^a,c   Pérez Abreu, Victor ^b  

^a AARHUS UNIVERSITY   (Denmark)

^b Ctr de Invest en Matematicas   (Mexico)

^c Department of Mathematical Sciences ^*  (Denmark)

Author keywords

Fractal spectral density; Normal inverse gaussian; Second order stationary increments; Type g

Indexed keywords

EID: 0033474816     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(99)00061-7     Document Type: Article

References (19)

1. Barndorff-Nielsen, O.E., 1977. Exponentially decreasing distributions for the logarithm of particle size. Proc. Roy. Soc. London A 353, 401-419.
2. Barndorff-Nielsen, O.E., 1979. Models for non-gaussian variation; with applications to turbulence. Proc. Roy. Soc. London A 368, 501-520.
3. Barndorff-Nielsen, O.E., 1982. The hyperbolic distribution in statistical physics. Scand. J. Statist. 9, 43-46.
4. Barndorff-Nielsen, O.E., 1998. Processes of normal inverse gaussian type. Finance Stochast. 2, 41-68.
5. Barndorff-Nielsen, O.E., Blæsild, P., Jensen, J.E., Sørensen, M., 1985. The fascination of sand. In: Atkinson, A.C., Fienberg, S.E. (Eds.), A Celebration of Statistics Centenary Volume of the ISI, Springer, Heidelberg, pp. 57-87.
6. Barndorff-Nielsen, O.E., Christiansen, C., 1985. Erosion, deposition and size distributions of sand. Proc. Roy. Soc. London A 417, 335-352.
7. Barndorff-Nielsen, O.E., Jensen, J.E., Sørensen, M., 1989. Wind shear and hyperbolic distributions. Boundary-layer Meteorol. 46, 417-431.
8. Barndorff-Nielsen, O.E., Jensen, J.E., Sørensen, M., 1990. Parametric modelling of turbulence. Philos. Trans. Roy. Soc. London A 332, 439-455.
9. Cramér, H., Leadbetter, M.R., 1967. Stationary and Related Stochastic Processes. Wiley, New York.
10. Eberlein, E., Keller, U., 1995. Hyperbolic distributions in finance. Bernoulli 1, 281-299.
11. Feller, W., 1971. An Introduction to Probability Theory and its Applications, Vol. 2, 2nd Edition. Wiley, New York.
12. Gradshteyn, I.S., Ryzhik, I.W., 1965. Table of Integrals, Series and Products. Academic Press, New York.
13. Lamperti, J.W., 1962. Semi-stable stochastic processes. Trans. Amer. Math. Soc. 104, 62-78.
14. Rajput, B., Rosinski, J., 1989. Spectral representations of infinite divisible processes. Probab. Theory Rel. Fields 82, 451-487.
15. Rosinski, J., 1991. On a class of infinitely divisible processes represented as mixtures of gaussian processes. In: Cambanis, S., Samorodnitsky, G., Taqqu, M.S. (Eds.), Stable Processes and Related Topics. Birkhäuser, Basel, pp. 27-41.
16. Rydberg, T., 1997a. The normal inverse gaussian lévy process: Simulation and approximation. Comm. Statist.: Stochastic Models 13, 887-910.
17. Rydberg, T., 1997b. Existence of unique equivalent martingale measures in a markovian setting. Finance Stochast. 1, 251-257.
18. Rydberg, T., 1999. Generalized hyperbolic diffusions with applications towards finance. Math. Finance 9, 183-201.
19. Samorodnitsky, G., Taqqu, M.S., 1994. Stable Non-gaussian Random Processes. Chapman & Hall, New York.