Limits for weighted p-variations and likewise functionals of fractional diffusions with drift

Stochastic Processes and their Applications

Volumn 117, Issue 3, 2007, Pages 271-296

  León, José ^a   Ludeña, Carenne ^b  

^a UNIVERSIDAD CENTRAL DE VENEZUELA   (Venezuela)

^b INSTITUTO VENEZOLANO DE INVESTIGACIONES CIENTÍFICAS   (Venezuela)

Author keywords

Fractional Brownian motion; Fractional diffusions; p variations

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; DIFFUSION; POLYNOMIALS;

FRACTIONAL BROWNIAN MOTION; FRACTIONAL DIFFUSIONS; HURST CONSTANT; MULTIPLICATIVE STRUCTURE; WEIGHTED P-VARIATIONS;

BROWNIAN MOVEMENT;

EID: 33846550201     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2006.05.016     Document Type: Article

References (23)

1. Arcones M. Limit theorems for nonlinear functionals of stationary Gaussian sequence of vectors. Ann. Probab. 22 (1994) 2242-2274
2. Breuer P., and Major P. Central limit theorems for non-linear functionals of Gaussian fields. J. Multivariate Anal. 13 (1983) 425-441
3. Billingsley P. Convergence of Probability Measures (1968), Wiley, New York
4. Cutland N., Kopp P.E., and Willinger W. Stock price returns and the Joseph effect: A fractional version of the Black Scholes model. Seminar on Stochastic Analysis, Random Fields and Applications, Ascona, 1993. Progress in Probability vol. 36 (1995), Birkhäuser, Verlag Basel/Switzerland 327-351
5. Decreusefond L. Stochastic integration with respect to fractional Brownian motion. Collect.: Theory Appl. Long-Range Depend. (2003) 203-226
6. Decreusefond L., and Ustünel A. Stochastic analysis of the fractional Brownian motion. Potential Anal. 10 2 (1999) 177-214
7. Fernique X.M. Régularité des fonctions aléatoires gaussiennes. École d'été de probabilités de Saint Flour. L.N.M. 480 (1974) 1-96
8. Florens-Zmirou D. On estimating the diffusion coefficient from discrete observations. J. Appl. Probab. 30 (1993) 790-804
9. Garcia A., Rademich E., and Rumsey H. A real variable lemma and the continuity of paths of some Gaussian processes. Indiana Univ. Math. J. 20 (1970) 565-578
10. Genon-Catalot V., and Jacod J. On the estimation of the diffusion coefficient for multi-dimensional diffusion processes. Ann. Inst. H. Poincaré 28 4 (1992) 119-151
11. Gloter A., and Hoffmann M. Stochastic volatility and fractional Brownian motion. Stochastic Process. Appl. 113 1 (2004) 143-172
12. Hall P., and Heyde C.C. Martingale limit theory and its applications. Probability and Mathematical Statistics (1980), Academic Press
13. Jacod J. On Continuous Conditional Gaussian Martingales and Stable Convergence in Law. LNM #1655, Seminaire de Prob. XXXI (1997) 232-246
14. Jacod J. Non-parametric kernel estimation of the diffusion coefficient of a diffusion. Scand. J. Statist. 27 1 (2000) 83-96
15. Klingenhöfer F., and Zähle M. Ordinary differential equations with fractal noise. Proc. Amer. Math. Soc. 127 4 (1999) 1021-1028
16. León J.R., and Ludeña C. Stable convergence of certain functionals of diffusions driven by fBm. Stochastic Anal. Appl. 22 (2004) 289-314
17. Lyons T. Differential equations driven by rough signals (I): An extension of an inequality of L.C. Young. Math. Res. Lett. 1 4 (1994) 451-464
18. Móricz F.A., Serfling R.J., and Stout W.F. Moment and probability bounds with quasi-supperadditive structure for the maximum partial sum. Ann. Probab. 10 4 (1989) 1032-1040
19. Norros I., Valkeila E., and Vitarmo J. An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions. Bernoulli 5 4 (1999) 571-587
20. Nualart D., and Rascanu A. Differential equations driven by fractional brownian motion. Collect. Math. 53 1 (2002) 55-81
21. Taqqu M. Law of the iterated logarithm for sums of non linear functions of Gaussian variables that exhibit long range dependence. Z. Wahrscheinlichkeistheorie verw. Gebiete 40 (1977) 203-238
22. Young L.C. An inequality of Hölder type, connected with Stieltjes integration. Acta Math. 67 (1936) 251-282
23. Zähle M. Integration with respect to fractal functions and stochastic calculus. I. Probab. Theory Related Fields 111 3 (1998) 333-374