Lévy-based spatial-temporal modelling, with applications to turbulence

Russian Mathematical Surveys

Volumn 59, Issue 1, 2004, Pages 65-90

  Barndorff Nielsen, O E ^a   Schmiegel, J ^a  

^a AARHUS UNIVERSITY   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042776069     PISSN: 00360279     EISSN: 14684829     Source Type: Journal    
DOI: 10.1070/RM2004v059n01ABEH000701     Document Type: Article

References (57)

1. O. E. Barndorff-Nielsen, "Probability and statistics; selfdecomposability, finance and turbulence", Proc. Conference "Probability towards 2000" (New York, 1995) (L. Accardi and C. C. Heyde, eds.), (Lecture Notes in Statist., vol. 128) Springer-Verlag, New York 1998, pp. 47-57.
2. O. E. Barndorff-Nielsen, "Processes of normal inverse Gaussian type", Finance Stochastics 2:1 (1998), 41-68.
3. O. E. Barndorff-Nielsen, "Superposition of Ornstein-Uhlenbeck type processes", Teor. Veroyatnost. i Primenen. 45 (2001), 289-311; reprint, Theory Probab. Appl. 45 (2001), 175-194.
4. O. E. Barndorff-Nielsen, "Superposition of Ornstein-Uhlenbeck type processes", Teor. Veroyatnost. i Primenen. 45 (2001), 289-311; reprint, Theory Probab. Appl. 45 (2001), 175-194.
5. O. E. Barndorff-Nielsen, "Modelling by Lévy processes", Selected Proc. Symposium on Inference for Stochastic Processes (Athens, 2000) (I. V. Basawa, C. C. Heyde, and R. L. Taylor, eds.), (IMS Lecture Notes Monogr. Ser., vol. 37) Inst. Math. Statist., Beachwood 2001, pp. 25-31.
6. O. E. Barndorff-Nielsen, J. L. Jensen, and M. Sørensen, "Parametric modelling of turbulence", Philos. Trans. Roy. Soc. London A 332 (1990), 439-455.
7. O. E. Barndorff-Nielsen, J. L. Jensen, and M. Sørensen, "A statistical model for the streamwise component of a turbulent velocity field", Ann. Geophys. 11 (1993), 99-103.
8. O. E. Barndorff-Nielsen, J. Pedersen, and K. Sato, "Multivariate subordination, selfdecomposability and stability", Adv. in Appl. Probab. 33 (2001), 160-187.
9. O. E. Barndorff-Nielsen and J. Schmiegel, "Lévy-based spatial-temporal modelling", in preparation, 2003.
10. O. E. Barndorff-Nielsen and N. Shephard, "Modelling by Lévy processes for financial econometrics", Lévy Processes - Theory and Applications (O. E. Barndorff-Nielsen, T. Mikosch, and S. Resnick, eds.), Birkhäuser, Boston 2001, pp. 283-318.
11. O. E. Barndorff-Nielsen and N. Shephard, "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics", J. R. Stat Soc. Ser. B Stat. Methodol. 63 (2001), 167-241.
12. O. E. Barndorff-Nielsen and N. Shephard, "Normal modified stable processes", Theory Probab. Math. Statist. 65 (2001), 1-20.
13. O. E. Barndorff-Nielsen and N. Shephard, "Integrated OU processes and non-Gaussian OU-based stochastic volatility models", Scand. J. Statist. 30 (2003), 277-295.
14. O. E. Barndorff-Nielsen and N. Shephard, Financial volatility: Stochastic volatility and Lévy based models, Cambridge Univ. Press, Cambridge 2004.
15. O. E. Barndorff-Nielsen and S. Thorbjørnsen, "A connection between classical and free infinite divisibility", Research Report 2003-7, University of Aarhus, MaPhySto, Aarhus 2003.
16. T. Bohr, M. H. Jensen, G. Paladin, and A. Vulpiani, Dynamical systems approach to turbulence, (Cambridge Nonlinear Science Series, vol. 8) Cambridge Univ. Press, Cambridge 1998.
17. A. Brix, Spatial and spatio-temporal models for weed abundance, PhD Thesis, Royal Veterinary and Agricultural University, Copenhagen 1998.
18. A. Brix, "Generalized gamma measures and shot-noise Cox processes", Adv. in Appl. Probab. 31 (1999), 929-953.
19. A. Brix and J. Chadœuf, "Spatio-temporal modelling of weeds by shot-noise G Cox processes", Biom. J. 44 (2002), 83-99.
20. A. Brix and P. J. Diggle, "Spatiotemporal prediction for log-Gaussian Cox processes", J. R. Stat. Soc. Ser. B Stat. Methodol. 63 (2001), 823-841.
21. M. Çag̃lar and E. Çinlar, "Lyapunov exponents of Poisson shot-noise velocity fields", Stochastic Process. Appl. 94:1 (2001), 29-49.
22. P. Carmona, F. Petit, and M. Yor, "Exponential functionals of Lévy processes", Lévy Processes - Theory and Applications (O. E. Barndorff-Nielsen, T. Mikosch, and S. Resnick, eds.), Birkhäuser, Boston 2001, pp. 41-55.
23. J. Cleve and M. Greiner, "The Markovian metamorphosis of a simple turbulent cascade model", Phys. Lett. A 273 (2000), 104-108.
24. D. Duffie, D. Filipović, and W. Schachermayer, "Affine processes and applications in finance", Ann. Appl. Probab. 13 (2003), 984-1053.
25. H. C. Eggers, T. Dziekan, and M. Greiner, "Translationally invariant cumulants in energy cascade models of turbulence", Phys. Lett. A 281 (2001), 249-255.
26. U. Frisch, Turbulence. The legacy of A. N. Kolmogorov, Cambridge Univ. Press, Cambridge 1995.
27. S. Ghashgaie, W. Breymann, J. Peinke, P. Talkner, and Y. Dodge, "Turbulent cascades in foreign exchange markets", Nature 381 (1996), 767-770.
28. M. Greiner, "Turbulent random multiplicative branching processes", Lectures on Multiscale and Multiplicative Processes in Fluid Flows (E. Waymire et al., eds.), (MaPhySto Lecture Notes, no. 11) MaPhySto, University of Aarhus, Aarhus 2002, pp. 81-88.
29. B. Jørgensen, The theory of dispersion models, Chapman and Hall, London 1997.
30. B. Jouault, M. Greiner, and P. Lipa, "Fix-point multiplier distributions in discrete turbulent cascade models", Phys. D 136 (2000), 125-144.
31. O. Kallenberg, Random measures, Akademie-Verlag, Berlin 1986.
32. A. N. Kolmogorov, "The local structure of turbulence in an incompressible viscous fluid for very large Reynolds numbers", Dokl. Akad. Nauk. SSSR 30 (1941), 299-303; English transl., Proc. Roy. Soc. London Ser. A 434 (1991), 9-13.
33. A. N. Kolmogorov, "The local structure of turbulence in an incompressible viscous fluid for very large Reynolds numbers", Dokl. Akad. Nauk. SSSR 30 (1941), 299-303; English transl., Proc. Roy. Soc. London Ser. A 434 (1991), 9-13.
34. A. N. Kolmogorov, "Dissipation of energy in locally isotropic turbulence", Dokl. Akad. Nauk. SSSR 32 (1941), 19-21; English transl., Selected works of A. N. Kolmogorov, vol. I: Mathematics and mechanics, Kluwer, Dordrecht 1991, pp. 328-330.
35. A. N. Kolmogorov, "Dissipation of energy in locally isotropic turbulence", Dokl. Akad. Nauk. SSSR 32 (1941), 19-21; English transl., Selected works of A. N. Kolmogorov, vol. I: Mathematics and mechanics, Kluwer, Dordrecht 1991, pp. 328-330.
36. A. N. Kolmogorov, "A refinement of the concept of the local structure of turbulence in a viscous incompressible fluid at high Reynolds numbers", Mécanique de la Turbulence (Actes du Colloque International du CNRS, Marseilles, August-September 1961), Paris, 1962, pp. 447-451; English transl., J. Fluid Mech. 13 (1962), 82-85.
37. A. N. Kolmogorov, "A refinement of the concept of the local structure of turbulence in a viscous incompressible fluid at high Reynolds numbers", Mécanique de la Turbulence (Actes du Colloque International du CNRS, Marseilles, August-September 1961), Paris, 1962, pp. 447-451; English transl., J. Fluid Mech. 13 (1962), 82-85.
38. S. Kwapień and W. A. Woyczyński, Random series and stochastic integrals: Single and multiple, Birkhäuser, Boston 1992.
39. C. Meneveau and K. R. Sreenivasan, "The multifractal nature of turbulent energy dissipation", J. Fluid Mech. 224 (1991), 429-484.
40. J. Møller, "Shot noise Cox processes", Research Report no. 2002-18, MaPhySto, University of Aarhus, Aarhus 2002.
41. J. Møller, A. R. Syversveen, and R. P. Waagepetersen, "Log Gaussian Cox processes", Scand. J. Statist. 25 (1998), 451-482.
42. A. S. Monin and A. M. Yaglom, Statistical fluid mechanics, vols. I, II, Nauka, Moscow 1965, 1967; English transl., MIT Press, Cambridge 1971.
43. E. Nicolato and E. Venardos, "Option pricing in stochastic volatility models of the Ornstein-Uhlenbeck type", Math. Finance 13 (2003), 445-466.
44. A. M. Obukhov, "Some specific features of atmospheric turbulence", J. Fluid Mech. 13 (1962), 77-81.
45. J. Pedersen, "The Lévy-Ito decomposition of an independently scattered random measure", Research Report no. 2003-2, MaPhySto, University of Aarhus, Aarhus 2003.
46. B. Rüdiger, "Stochastic integration with respect to compensated Poisson random measures on separable Banach spaces", Research Report, SFB 611, Universität Bonn, Bonn 2003.
47. G. Samorodnitsky and M. Taqqu, Stable non-Gaussian random processes, Chapman and Hall, New York 1994.
48. K. Sato, Lévy processes and infinitely divisible distributions, Cambridge Univ. Press, Cambridge 1999.
49. W. Schoutens, Lévy processes in finance, Wiley, New York 2003.
50. J. Schmiegel, Ein dynamischer Prozess für die statistische Beschreibung der Energiedissipation in der vollentwickelten Turbulenz, dissertation, TU Dresden, Dresden 2002.
51. J. Schmiegel, "Some remarks on Taylor's frozen flow hypothesis", Research Report, MaPhySto, University of Aarhus, Aarhus 2003.
52. J. Schmiegel, T. Dziekan, J. Cleve, B. Jouault, and M. Greiner, "Scaling functions in a random multiplicative energy-cascade model of turbulence", Phys. Rev. E (2002) (to appear).
53. J. Schmiegel, H. C. Eggers, and M. Greiner, "Dynamical random multiplicative cascade model in 1 + 1 dimensions", Preprint, cond-mat/0106347, 2001.
54. J. Schmiegel, H. C. Eggers, and M. Greiner, "A spatio-temporal and causal multifractal stochastic process", Phys. A (2003) (to appear).
55. A. N. Shiryaev, "Kolmogorov and the turbulence", (Miscellanea, no. 12) MaPhySto, University of Aarhus, Aarhus 1999.
56. K. R. Sreenivasan and R. A. Antonia, "The phenomenology of small-scale turbulence", Annu. Rev. Fluid Mech. 29 (1997), 435-472.
57. R. L. Wolpert and K. Ickstadt, "Poisson/gamma random field models for spatial statistics", Biometrika 85 (1998), 251-267.