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Lectures and exercises are devoted to stochastic processes with continuous time and to the basics of stochastic
calculus.
Last update: Omelka Marek, doc. Ing., Ph.D. (16.02.2023)
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Students will broaden their knowledge about stochastic processes with continuous time and they will get acquainted with basics results of stochastic calculus. Last update: Čoupek Petr, RNDr., Ph.D. (16.02.2023)
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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. Last update: Čoupek Petr, RNDr., Ph.D. (16.02.2023)
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[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. Last update: Čoupek Petr, RNDr., Ph.D. (16.02.2023)
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Lecture and exercises. Last update: Čoupek Petr, RNDr., Ph.D. (16.02.2023)
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The requirements correspond to the syllabus of the course to the extent in which it was presented during the lectures. Last update: Čoupek Petr, RNDr., Ph.D. (23.02.2023)
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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 Last update: Čoupek Petr, RNDr., Ph.D. (23.02.2023)
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Basic knowledge of proability theory (modes of convergence for random variables, conditional expectation, etc.) and theory of stochastic processes (martingales with discrete time). Last update: Čoupek Petr, RNDr., Ph.D. (16.02.2023)
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