|
|
|
||
Last update: T_KPMS (17.05.2013)
|
|
||
Last update: T_KPMS (17.05.2013)
Introduction to continuous-time martingales and semimartingales. Variation of stochastic process, contruction and application of martingale stochastic integral with emphasis to survival analysis. |
|
||
Last update: T_KPMS (17.05.2013)
Fleming, T.R., Harrington, D.P.: Counting processes and survival analysis. John Wiley & Sons, Inc., New York, 1991 Steele, J.M.: Stochastic calculus and financial applications. Springer, New York, 2001 |
|
||
Last update: T_KPMS (16.05.2013)
Lecture. |
|
||
Last update: doc. Mgr. Petr Kaplický, Ph.D. (10.06.2015)
1. Continuous time stochastic processes, counting processes, martingales.
2. Cummulative risk function, risk intensity, independent censoring, compensator.
3. Doob-Meyer decomposition, predictability, predictable quadratic variation.
4. Stochastic integral with respect to a bounded variation martingales, predictable variation and covariation of stochastic integral.
5. Martingale central limit theorems, functional central limit theorem, Gaussian processes.
6. Localization and local martingales. |