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Continuous-time martingales. Predictability. Doob-Meyer decomposition of semimartingales. Counting processes
and compensators. Predictable variation. Martingale stochastic integrals. Central limit theorem for martingale
stochastic integrals.
Last update: T_KPMS (17.05.2013)
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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)
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Final oral exam. Update for the academic year 2019/2020: the oral exam may be done using on-line connection in the case of need. Last update: Hlubinka Daniel, doc. RNDr., Ph.D. (23.04.2020)
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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 (17.05.2013)
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Lecture. Last update: T_KPMS (16.05.2013)
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The final exam is oral. It consists of a few questions covering the topic of the lectures. Last update: Hlubinka Daniel, doc. RNDr., Ph.D. (26.02.2018)
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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. Last update: Kaplický Petr, doc. Mgr., Ph.D. (10.06.2015)
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Knowledge required before enrollment: conditional probability and conditional expectation discrete martingales central limit theorem Last update: Hlubinka Daniel, doc. RNDr., Ph.D. (10.05.2018)
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