Time change, volatility, and turbulence

Mathematical Control Theory and Finance

Volumn , Issue , 2008, Pages 29-53

  Barndorff Nielsen, Ole E ^a   Schmiegel, Jürgen ^a  

^a AARHUS UNIVERSITY   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84895275647     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-540-69532-5_3     Document Type: Chapter

References (52)

1. Andersen TG, Bollerslev T, Diebold FX, Ebens H (2001) The distribution of realized stock return volatility. J. Fin. Econometrics, 61:43-76.
2. Andersen TG, Bollerslev T, Frederiksen PH, Nielsen M. (2006) Continuoustime models, realized volatilities, and testable distributional implications for daily stock returns. Unpublished paper.
3. Asmussen S, Rosinski J (2001) Approximation of small jumps of Levy processes with a view towards simulation. J. Appl. Probab., 38:482-493.
4. Barndorff-Nielsen OE (1977) Exponentially decreasing distributions for the logarithm of particle size. Proc. R. Soc. London A 353:401-419.
5. Barndorff-Nielsen OE (1995) Normal inverse Gaussian processes and the modelling of stock returns. Research Report 300, Dept. Theor. Statistics, Aarhus University.
6. Barndorff-Nielsen OE (1997) Normal inverse Gaussian distributions and stochastic volatility modelling. Scand. J. Statist., 24:1-14.
7. Barndorff-Nielsen OE (1998) Probability and statistics: self-decomposability, finance and turbulence. In: Acccardi L, Heyde CC (Eds) Probability Towards 2000, 47-57. Proceedings of a Symposium held 2-5 October 1995 at Columbia University. Springer-Verlag, New York
8. Barndorff-Nielsen OE (1998) Processe of normal inverse Gaussian type. Finance and Stochastics, 2:41-68.
9. Barndorff-Nielsen OE (1998) Superposition of Ornstein-Uhlenbeck type processes. Theory Prob. Its Appl., 45:175-194.
10. Barndorff-Nielsen OE, Blild P, Schmiegel J (2004) A parsimonious and universal description of turbulent velocity increments. Eur. Phys. J., B 41:345-363.
11. Barndorff-Nielsen OE, Graversen SE, Jacod J, Podolskij M, Shephard N (2006) A central limit theorem for realised power and bipower variations of continuous semimartingales. In: Kabanov Yu, Liptser R, Stoyanov J (Eds) From Stochastic Calculus to Mathematical Finance 33-68. Festschrift in Honour of A.N. Shiryaev. Springer, Heidelberg
12. Barndorff-Nielsen OE, Graversen SE, Jacod J, Shephard N (2006) Limit theorems for bipower variation in financial econometrics. Econometric Theory, 22:677-719.
13. Barndorff-Nielsen OE, Levendorskii SZ (2001) Feller processes of normal inverse Gaussian type. Quantitative Finance, 1:318-331.
14. Barndorff-Nielsen OE, Prause K (2001) Apparent scaling. Finance and Stochastics, 5:103-113.
15. Barndorff-Nielsen OE, Schmiegel J (2004) Levy-based tempo-spatial modelling; with applications to turbulence. Uspekhi Mat. Nauk., 59:65-91.
16. Barndorff-Nielsen OE, Schmiegel J (2006) A stochastic differential equation framework for the timewise dynamics of turbulent velocities. Theory of Probability and its Applications. (To appear
17. Barndorff-Nielsen OE, Schmiegel J (2006) Time change and universality in turbulence. (Submitted
18. Barndorff-Nielsen OE, Schmiegel J. (2007) Ambit processes; with applications to turbulence and cancer growth. Proceedings of the 2005 Abel Symposium on Stochastic Analysis and Applications. Springer, Heidelberg (To appear
19. Barndorff-Nielsen OE, Schmiegel J (2007) Change of time and universal laws in Turbulence. (Submitted
20. Barndorff-Nielsen OE, Schmiegel J, Shephard N (2006) Time change and universality in turbulence and finance. (Submitted
21. Barndorff-Nielsen OE, Schmiegel J, Shephard N (2007) QV, BV and VR under stationary Gaussian processes. (In preparation
22. Barndorff-Nielsen OE, Shephard N (2001) Modelling by Levy processes for financial econometrics. In: Barndorff-Nielsen OE, Mikosch T, Resnick S (Eds) Levy Processes - Theory and Applications, 283-318. Birkhauser, Boston
23. Barndorff-Nielsen OE, Shephard N (2001) Non-Gaussian Ornstein- Uhlenbeckbased models and some of their uses in financial economics (with Discussion). J. R. Statist. Soc., B 63:167-241.
24. Barndorff-Nielsen OE, Shephard N (2002) Integrated OU processes and non-Gaussian OU-based stochastic volatility. Scand. J. Statist., 30:277-295.
25. Barndorff-Nielsen OE, Shephard N (2004) Power and bipower variation with stochastic volatility and jumps (with Discussion). J. Fin. Econometrics, 2:1-48.
26. Barndorff-Nielsen OE, Shephard N (2008) Financial Volatility in Continous Time. Cambridge University Press. (To appear
27. Barndorff-Nielsen OE, Shiryaev AN (2008) Change of Time and Change of Measure. World Scientific, Singapore (To appear
28. Bender C, Marquardt T (2007) Stochastic calculus for convoluted Levy processes. (Unpublished manuscript
29. Castaing B, Gagne Y, Hopfinger EJ (1990) Velocity probability density functions of high Reynolds number turbulence. Physica, D 46:177-200.
30. Cont R, Tankov P (2004) Financial Modelling With Jump Processes. Chapman& Hall/CRC, London
31. Decreusefond L (2005) Stochastic integration with respect to Volterra processes. Ann. I. H. Poincare, PR41:123-149.
32. Decreusefond L, Savy N (2006) Anticipative calculus with respect to filtered Poisson processes. Ann. I. H. Poincare, PR42:343-372.
33. Eberlein E (2000) Application of generalized hyperbolic Levy motion to finance. In: Barndorff-Nielsen OE, Mikosch T, Resnick S (Eds) Levy Processes - Theory and Applications, 319-336. Birkhauser, Boston
34. Elsner JW, Elsner W (1996) On the measurement of turbulence energy dissipation. Meas. Sci. Technol., 7:1334-1348.
35. Forsberg L (2002) On the Normal Inverse Gaussian distribution in Modelling Volatility in the Financial Markets. Acta Universitatis Upsaliemsis, Studia Statistica Upsaliensia 5, Uppsala.
36. Ghashgaie S, Breymann W, Peinke J, Talkner P, Dodge Y (1996) Turbulent cascades in foreign exchange markets. Nature 381:767-770.
37. Hult H (2003) Approximating some Volterra type stochastic intergrals with applications to parameter estimation. Stoch. Proc. Appl., 105:1-32.
38. Kolmogorov AN (1941) Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk. SSSR, 32:16-18.
39. Kolmogorov AN (1962) A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech, 13:82-85.
40. Marquardt T (2006) Fractional Levy processes with an application to long memory moving average processes. Bernoulli, 12:1099-1126.
41. McNeil AJ, Frey R, Embrechts P (2005) Quantitative Risk Management. Princton University Press, Princeton
42. Norros I, Valkeila E, Virtamo J (1999) An elementary approach to a Girsanov formula and other analytic results on fractional Brownian motion. Bernoulli, 5:571-587.
43. Obukhov AM (1962) Some specific features of atmospheric turbulence. J. Fluid Mech., 13:77-81.
44. Peinke J, Bottcher F, Barth S (2004) Anomalous statistics in turbulence, financial markets and other complex systems. Ann. Phys. (Leipzig), 13:450-460.
45. Prause K (1999) The Generalized Hyperbolic Model: Estimation, Financial Derivatives and Risk Measures. Dissertation, Albert-Ludwigs-Universitat, Freiburg i. Br.
46. Raible S (2000) Levy Processes in Finance: Theory, Numerics, Empirical Facts. Dissertation, Albert-Ludwigs-Universitat, Freiburg i. Br.
47. Rydberg TH (1997) The normal inverse Gaussian Levy process: simulation and approximation. Comm. Statist.: Stochastic Models, 13:887-910.
48. Rydberg TH (1999) Generalized hyperbolic diffusions with applications towards finance. Math. Finance, 9:183-201.
49. Samorodnitsky G, Taqqu MS (1994) Stable Non-Gaussian Random Processes. Chapman and Hall, New York
50. Shiryaev AN (2006) Kolmogorov and the turbulence. Research Report 2006-4. Thiele Centre for Applied Mathematics in Natural Science.
51. Shiryaev AN (2007) On the classical, statistical and stochastic approaches to hydrodynamic turbulence. Research Report 2007-2. Thiele Centre for Applied Mathematics in Natural Science.
52. Vincent A, Meneguzzi M (1991) The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech., 225:1-25.