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Last update: T_KPMS (15.05.2013)
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Last update: T_KPMS (15.05.2013)
To explain basics of the martingale theory. |
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Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (30.09.2021)
The course is finalized by a credit from exercise class and by a final exam.
The credit from exercise class is necessary for taking part in the final exam.
Requirements for receiving the credit from exercise class: active participation (attendance at least 75% during in-person classes), elaboration of two homeworks.
Attempt to receive the credit from exercise class cannot be repeated. |
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Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (28.10.2019)
J. Jacod, P. Protter (2004): Probability Essentials, 2nd edition, Springer, Berlin.
O. Kallenberg (2002): Foundations of Modern Probability, 2nd edition, Springer, New York.
J. Štěpán (1987): Teorie pravděpodobnosti - matematické základy, Academia, Praha. |
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Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (29.09.2021)
Lecture+exercises. |
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Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (11.10.2017)
The final exam is oral. All material covered during the course may be part of the exam. |
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Last update: T_KPMS (24.04.2015)
1. random sequence, finite-dimensional distributions, Daniell's theorem
2. filtration, stopping times, martingale (submartingale, supermartingale) with discrete time
3. optional stopping and optional sampling theorem, maximal inequalities
4. convergence of submartingales
5. limit theorems for martingale differences |
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Last update: doc. RNDr. Zbyněk Pawlas, Ph.D. (18.05.2018)
Basics of probability theory - probability space, random vectors, independence, convergence, conditional expectation, characteristic function, law of large numbers, central limit theorem. |