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Last update: doc. Ing. Marek Omelka, Ph.D. (16.02.2023)
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Last update: RNDr. Petr Čoupek, Ph.D. (16.02.2023)
Students will broaden their knowledge about stochastic processes with continuous time and they will get acquainted with basics results of stochastic calculus. |
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Last update: RNDr. Petr Čoupek, Ph.D. (16.02.2023)
Students need to obtain the credit for the exercise class and pass an exam. To take the exam, it is necessary to obtain the credit for the exercise class first. Students can obtain the credit for the exercise class by submitting their own sufficiently worked-out solutions of 3 homework problems by the specified deadlines. The nature of this condition prevents retry. |
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Last update: RNDr. Petr Čoupek, Ph.D. (16.02.2023)
[1] Karatzas, I., Shreve, D.E.: Brownian Motion and Stochastic Calculus. Springer, New York, ed. 2, 1998. [2] Revuz, D., Yor, M.: Continuous Martingales and Brownian Motion, Springer-Verlag Berlin Heidelberg, ed. 3, 1999. [3] Protter, P.E.: Stochastic Integration and Differential Equations, Spriner-Verlag Berlin Heidelberg, ed. 2, 2004. [4] Le Gall, J.-F.: Brownian Motion, Martingales, and Stochastic Calculus, Springer Cham, ed. 1, 2016. |
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Last update: RNDr. Petr Čoupek, Ph.D. (16.02.2023)
Lecture and exercises. |
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Last update: RNDr. Petr Čoupek, Ph.D. (23.02.2023)
The requirements correspond to the syllabus of the course to the extent in which it was presented during the lectures. |
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Last update: RNDr. Petr Čoupek, Ph.D. (23.02.2023)
1. Stochastic processes with continuous time 2. Wiener process 3. Filtrations and stopping times 4. Martingales with continuous time 5. Local martingales 6. Continuous semimartingales 7. Stochastic integral and Ito’s formula 8. Stochastic differential equations |
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Last update: RNDr. Petr Čoupek, Ph.D. (16.02.2023)
Basic knowledge of proability theory (modes of convergence for random variables, conditional expectation, etc.) and theory of stochastic processes (martingales with discrete time). |