Measure, Probability and Functional Analysis by Geiss, Hannah; Geiss, Stefan;

Sorozatcím: Universitext;

12% KEDVEZMÉNY?

Kiadói listaár EUR 64.19
Az ár azért becsült, mert a rendelés pillanatában nem lehet pontosan tudni, hogy a beérkezéskor milyen lesz a forint árfolyama az adott termék eredeti devizájához képest. Ha a forint romlana, kissé többet, ha javulna, kissé kevesebbet kell majd fizetnie.

26 622 Ft (25 355 Ft + 5% áfa)
Kedvezmény(ek) 12% (cc. 3 195 Ft off)
Kedvezményes ár 23 428 Ft (22 312 Ft + 5% áfa)

23 428 Ft

Beszerezhetőség

Megrendelésre a kiadó utánnyomja a könyvet. Rendelhető, de a szokásosnál kicsit lassabban érkezik meg.

A termék adatai:

Kiadó Springer Nature Switzerland
Megjelenés dátuma 2025. március 26.
Kötetek száma 1 pieces, Book

ISBN 9783031840661
Kötéstípus Puhakötés
Terjedelem443 oldal
Méret 235x155 mm
Nyelv angol
Illusztrációk XX, 443 p. 18 illus., 14 illus. in color. Illustrations, black & white

Kategóriák

Analízis Valószínűségelmélet és matematikai statisztika Alkalmazott matematika

Hosszú leírás:

This textbook offers a self-contained introduction to probability, covering all topics required for further study in stochastic processes and stochastic analysis, as well as some advanced topics at the interface between probability and functional analysis.

The initial chapters provide a rigorous introduction to measure theory, with a special focus on probability spaces. Next, Lebesgue integration theory is developed in full detail covering the main methods and statements, followed by the important limit theorems of probability. Advanced limit theorems, such as the Berry-Esseen Theorem and Stein’s method, are included. The final part of the book explores interactions between probability and functional analysis. It includes an introduction to Banach function spaces, such as Lorentz and Orlicz spaces, and to random variables with values in Banach spaces. The Itô–Nisio Theorem, the Strong Law of Large Numbers in Banach spaces, and the Bochner, Pettis, and Dunford integrals are presented. As an application, Brownian motion is rigorously constructed and investigated using Banach function space methods.

Based on courses taught by the authors, this book can serve as the main text for a graduate-level course on probability, and each chapter contains a collection of exercises. The unique combination of probability and functional analysis, as well as the advanced and original topics included, will also appeal to researchers working in probability and related fields.

Több

Tartalomjegyzék:

- 1. Introduction – with two examples.- 2. Measure spaces and probability spaces.- 3. Construction of measure spaces.- 4. *Metric and Banach spaces.- 5. *Measures on metric spaces.- 6. Random variables and measurable maps.- 7. Independence.- 8. Integration.- 9. Convergence of random variables.- 10. The theorem of Radon-Nikodym and conditional expectation.- 11. Fourier transform and Gaussian distributions.- 12. Weak convergence.- 13. Strong law of large numbers.- 14. An ergodic theorem.- 15. Limit theorems for weak convergence.- 16. Fourier inversion formulas.- 17. Norm estimates for the Fourier transform.- 18. Riesz representation theorems.- 19. Banach function spaces.- 20. Probability in Banach spaces.- 21. Law of iterated logarithm.- 22. An application to non-life insurance.