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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)
An advanced lecture on Brownian motion and stochastic integral is designed to to complete a student knowledge and abilities to handle a stochastic process both from theoretical and applied view. |
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Last update: RNDr. Petr Čoupek, Ph.D. (16.02.2023)
Dupačová, J., Hurt, J., Štěpán, J.: Stochastic Modeling in Economics and Finance. Kluwer Academic Publishers, London, 2002.
O. Kallenberg: Foundations of modern probability. Springer, New York, 2002.
Karatzas, I., Shreve, D.E.: Brownian Motion and Stochastic Calculus. Springer Verlag, New York, 1991.
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Last update: RNDr. Petr Čoupek, Ph.D. (16.02.2023)
Lecture+exercises |
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Last update: RNDr. Petr Čoupek, Ph.D. (16.02.2023)
1. Stochastic processes and their construction.
2. Continuous martingales and Brownian motion.
3. Markov times, martingales stopped by a Markov time.
4. Spaces of stochastic processes.
5. Doob Meyer decomposition. Quadratic variation of a continuous martingale.
6. Stochastic integral and its properties.
7. Exponential martingales and Lévy characterization of Brownian motion.
8. Trend removing Girsanov theorem for Brownian motion.
9. Brownian representation of a continuous martingale by a stochastic integral.
10. Local time of a continuous martingale.
11. An introduction to the theory of stochastic differential equations.
12. Stochastic analysis applied to physics and financial mathematics.
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