Stochastické diferenciální rovnice s gaussovským šumem a jejich aplikace
| Thesis title in Czech: | Stochastické diferenciální rovnice s gaussovským šumem a jejich aplikace |
|---|---|
| Thesis title in English: | Stochastic Differential Equations with Gaussian Noise and Their Applications |
| Key words: | stochastické diferenciální rovnice, frakcionální Brownův pohyb |
| English key words: | stochastic differential equations, fractional Brownian motion |
| Academic year of topic announcement: | 2019/2020 |
| Thesis type: | diploma thesis |
| Thesis language: | čeština |
| Department: | Department of Probability and Mathematical Statistics (32-KPMS) |
| Supervisor: | RNDr. Petr Čoupek, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 27.08.2019 |
| Date of assignment: | 28.08.2019 |
| Confirmed by Study dept. on: | 27.02.2020 |
| Date and time of defence: | 07.09.2020 08:00 |
| Date of electronic submission: | 30.07.2020 |
| Date of submission of printed version: | 30.07.2020 |
| Date of proceeded defence: | 07.09.2020 |
| Opponents: | doc. RNDr. Jan Večeř, Ph.D. |
| Advisors: | prof. RNDr. Bohdan Maslowski, DrSc. |
| Guidelines |
| Tématem práce budou stochastické differenciální rovnice s gaussovským šumem různé regularity (příp. systémy takovýchto rovnic) a jejich aplikace na konkrétní problémy. Jako příklad takového problému lze uvést tzv. stochastický oscilátor. |
| References |
| [1] Biagini, F., Hu, Y., Oksendal, B., Zhang, T. Stochastic Calculus for Fractional Brownian Motion and Applications, Springer, 2008.
[2] Oksendal, B. Stochastic Differential Equations: An Introduction with Applications, 6th ed., Springer, 2003. [3] Duncan, T.E., Maslowski, B., Pasik-Duncan, B. Semilinear stochastic equations in a Hilbert space with fractional Brownian motion, SIAM J. Math. Anal. 40 (6), 2286-2315, 2009. [4] Šnupárková, J. Weak solutions to stochastic differential equations driven by fractional Brownian motion, Czech Math. J. 59 (4), 879-907, 2009. |