Geometric Aspects of Probability Theory and Mathematical Statistics: 514 - Brossura

Buldygin, V.V.; Kharazishvili, A.B.

Brossura

ISBN 10: 9048155053 ISBN 13: 9789048155057

Casa editrice: Springer, 2010

Riassunto

It is well known that contemporary mathematics includes many disci­ plines. Among them the most important are: set theory, algebra, topology, geometry, functional analysis, probability theory, the theory of differential equations and some others. Furthermore, every mathematical discipline consists of several large sections in which specific problems are investigated and the corresponding technique is developed. For example, in general topology we have the following extensive chap­ ters: the theory of compact extensions of topological spaces, the theory of continuous mappings, cardinal-valued characteristics of topological spaces, the theory of set-valued (multi-valued) mappings, etc. Modern algebra is featured by the following domains: linear algebra, group theory, the theory of rings, universal algebras, lattice theory, category theory, and so on. Concerning modern probability theory, we can easily see that the clas­ sification of its domains is much more extensive: measure theory on ab­ stract spaces, Borel and cylindrical measures in infinite-dimensional vector spaces, classical limit theorems, ergodic theory, general stochastic processes, Markov processes, stochastical equations, mathematical statistics, informa­ tion theory and many others.

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Contenuti

Preface. 1. Convex sets in vector spaces. 2. Brunn-Minkowski inequality. 3. Convex polyhedra. 4. Two classical isoperimetric problems. 5. Some infinite-dimensional vector spaces. 6. Probability measures and random elements. 7. Convergence of random elements. 8. The structure of supports of Borel measures. 9. Quasi-invariant probability measures. 10. Anderson inequality and unimodal distributions. 11. Oscillation phenomena and extensions of measures. 12. Comparison principles for Gaussian processes. 13. Integration of vector-valued functions and optimal estimation of stochastic processes. Appendices. Bibliography. Subject Index.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 9048155053
• ISBN 13: 9789048155057
• Rilegatura: Copertina flessibile
• Numero di pagine: 316
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania