Estimation in models driven by fractional brownian motion
Annales de l'I.H.P. Probabilités et statistiques (2008)
- Volume: 44, Issue: 2, page 191-213
- ISSN: 0246-0203
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] J.-M. Azaïs and M. Wschebor. Almost sure oscillation of certain random processes. Bernoulli 2 (1996) 257–270. Zbl0885.60018MR1416866
- [2] C. Berzin and J. R. León. Convergence in fractional models and applications. Electron. J. Probab. 10 (2005) 326–370. Zbl1070.60022MR2120247
- [3] C. Berzin and J. R. León. Estimating the Hurst parameter. Stat. Inference Stoch. Process. 10 (2007) 49–73. Zbl1110.62110MR2269604
- [4] N. J. Cutland, P. E. Kopp and W. Willinger. Stock price returns and the Joseph effect: A fractional version of the Black–Scholes model. In Seminar on Stochastic Analysis, Random Fields and Applications (Ascona, 1993) 327–351. Switzerland. Zbl0827.60021MR1360285
- [5] L. Decreusefond and A. S. Üstünel. Stochastic analysis of the fractional Brownian motion. Potential Anal. 10 (1999) 177–214. Zbl0924.60034MR1677455
- [6] A. Gloter and M. Hoffmann. Stochastic volatility and fractional Brownian motion. Stochastic Process. Appl. 113 (2004) 143–172. Zbl1065.62179MR2078541
- [7] F. Klingenhöfer and M. Zähle. Ordinary differential equations with fractal noise. Proc. Amer. Math. Soc. 127 (1999) 1021–1028. Zbl0915.34054MR1486738
- [8] S. J. Lin. Stochastic analysis of fractional Brownian motions. Stochastics Stochastics Rep. 55 (1995) 121–140. Zbl0886.60076MR1382288
- [9] T. Lyons. Differential equations driven by rough signals, I: An extension of an inequality of L. C. Young. Math. Res. Lett. 1 (1994) 451–464. Zbl0835.34004MR1302388
- [10] B. B. Mandelbrot and J. W. Van Ness. Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10 (1968) 422–437. Zbl0179.47801MR242239
- [11] D. Nualart and A. Răşcanu. Differential equations driven by fractional Brownian motion. Collect. Math. 53 (2001) 55–81. Zbl1018.60057MR1893308