Frakcionální Brownův pohyb
| Thesis title in Czech: | Frakcionální Brownův pohyb |
|---|---|
| Thesis title in English: | Fractional Brownian motion |
| Key words: | frakcionální Brownův pohyb, nediferencovatelnost trajektorií, si- mulace trajektorií, odhad Hurstova indexu |
| English key words: | fractional Brownian motion, nondifferentiability of paths, simulation of paths, estimator of Hurst parameter |
| Academic year of topic announcement: | 2012/2013 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | čeština |
| Department: | Department of Probability and Mathematical Statistics (32-KPMS) |
| Supervisor: | prof. RNDr. Bohdan Maslowski, DrSc. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 04.10.2012 |
| Date of assignment: | 05.10.2012 |
| Confirmed by Study dept. on: | 04.12.2012 |
| Date and time of defence: | 27.06.2013 00:00 |
| Date of electronic submission: | 23.05.2013 |
| Date of submission of printed version: | 24.05.2013 |
| Date of proceeded defence: | 27.06.2013 |
| Opponents: | Mgr. Ing. Pavel Kříž, Ph.D. |
| Advisors: | RNDr. Jana Šnupárková, Ph.D. |
| Guidelines |
| Student/ka uvede některé vlastnosti frakcionálního Brownova pohybu ve srovnání s Wienerovým procesem, seznámí se se základy látky z uvedené literatury a bude zpracovávat vybrané teoretické problémy. |
| References |
| [1] F. Biagini, Y. Hu, B. Oksendal, T. Zhang: Stochastic Calculus for Fractional Brownian Motion and Applications. Springer-Verlag, London, 2008
[2] I. Karatzas, S. E. Shreve: Brownian Motion and Stochastic Calculus. Springer-Verlag, New York, 1988 [3] D. Nualart: Stochastic integration with respect to fractional Brownian motion and applications. Stochastic models (Mexico City, 2002), Contemp. Math., 336, Amer. Math. Soc., Providence, RI, 2003 |