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Probability measures on metric spaces. Prokhoroff theorem. Properties of C[0,1] and D[0,1]. Donsker invariance
principle.
Last update: T_KPMS (20.04.2015)
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To teach and explain theory of convergence of random processes, especially in functional spaces C([0,1]) and D([0,1]). Last update: T_KPMS (16.05.2013)
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+--------------------------------------------------------------------------- Course finalization +--------------------------------------------------------------------------- The course is finalized by exam. Last update: Lachout Petr, doc. RNDr., CSc. (29.04.2020)
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Billingsley, P.: Convergence of Probability Measures, John Wiley & Sons,New York, 1968.
Čech, E.: Topologické prostory, Academia, Praha, 1959.
Kelley, J.L.: General Topology, D. van Nostrand Comp., New York, 1955.
Štěpán J.: Teorie pravděpodobnosti. Matematické základy. Academia, Praha 1987 Last update: T_KPMS (20.04.2015)
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Lecture. Last update: T_KPMS (16.05.2013)
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+--------------------------------------------------------------------------- Requirements to exam +--------------------------------------------------------------------------- The exam is oral. Examination is checking knowledge of all topics read at the lecture and parts given to self-study by the course lecturer.
Last update: Lachout Petr, doc. RNDr., CSc. (14.02.2024)
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1. Basic of topology (product and relativ topology, Tikhonov theorem, random maps, random variables, probability measures on topological spaces, weak convergence of probability measures).
2. Metric spaces (Polish space, Prokhorov theorem, Banach space).
3. Topology of the space of functions (Borel sigma-algebra, Daniell-Kolmogorov theorem, cylindric sigma-algebra, random process).
4. Properties of spaces C[0,1] and D[0,1],
5. Donsker invariance princip and applications.
Last update: T_KPMS (20.04.2015)
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measure and integration theory, probability theory, functional analysis Last update: Lachout Petr, doc. RNDr., CSc. (30.05.2018)
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