NMTP434 - Invariance Principles - lecture
Brief sylabus:
- Bases of topology, Borel sigma-algebra, relative topology, product topology, Tikhonoff's theorem, random mappings, random variables.
- Probability measures on topological spases, weak convergence of probability measures.
- Metric spaces - Polish space, Prokhoroff's theorem, Banach space.
- Topology of functional spaces - Daniell-Kolmogoroff theorem, cylindric sigma-algebra, random process.
- Space of continuous functions C[0,1], Donsker invariance principle in C[0,1].
- Skorokhod space of discontinuous functions D[0,1], Donsker invariance principle in D[0,1].
Literatura:
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
A text to the lecture:
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