Produktbild: Random Walk, Brownian Motion, and Martingales
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Random Walk, Brownian Motion, and Martingales

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

21.09.2021

Abbildungen

XV, 396 p. 20 illus.

Verlag

Springer

Seitenzahl

396

Maße (L/B/H)

24,1/16/2,7 cm

Gewicht

856 g

Sprache

Englisch

ISBN

978-3-030-78937-4

Beschreibung

Rezension

“The present text does an outstanding job of presenting many complementary aspects of the subject in a unified and coherent way … the subject matter and appreciation for the work of the authors in producing such an engaging and readable book. The authors suggest various models for graduate-level courses … . There is a great deal in the book that will be interesting, stimulating, and enjoyable for readers with an interest in probability theory and stochiastic processes.” (Andrew Wade, zbMATH 1489.60001, 2022)

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

21.09.2021

Abbildungen

XV, 396 p. 20 illus.

Verlag

Springer

Seitenzahl

396

Maße (L/B/H)

24,1/16/2,7 cm

Gewicht

856 g

Sprache

Englisch

ISBN

978-3-030-78937-4

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: GPSR Kontakt

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  • Produktbild: Random Walk, Brownian Motion, and Martingales
  • 1. What is a Stochastic Process?.- 2. The Simple Random Walk I: Associated Boundary Value Distributions, Transience and Recurrence.- 3. The Simple Random Walk II: First Passage Times.- 4. Multidimensional Random Walk.- 5. The Poisson Process, Compound Poisson Process, and Poisson Random Field.- 6. The Kolmogorov–Chentsov Theorem and Sample Path Regularity.- 7. Random Walk, Brownian Motion and the Strong Markov Property.- 8. Coupling Methods for Markov Chains and the Renewal Theorem for Lattice Distributions.- 9. Bienyamé–Galton–Watson Simple Branching Process and Extinction.- 10. Martingales: Definitions and Examples.- 11. Optional Stopping of (Sub)Martingales.- 12. The Upcrossings Inequality and (Sub)Martingale Convergence.- 13.- Continuous Parameter Martingales.- 14. Growth of Supercritical Bienyamé–Galton–Watson Simple Branching Processes.- 15. Stochastic Calculus for Point Processes and a Martingale Characterization of the Poisson Process.- 16. First Passage Time Distributions forBrownian Motion with Drift and a Local Limit Theorem.- 17. The Functional Central Limit Theorem (FCLT).- 18. ArcSine Law Asymptotics.- 19. Brownian Motion on the Half-Line: Absorption and Reflection.- 20. The Brownian Bridge.- 21. Special Topic: Branching Random Walk, Polymers and Multiplicative Cascades.- 22. Special Topic: Bienyamé–Galton–Watson Simple Branching Process and Excursions.- 23. Special Topic: The Geometric Random Walk and the Binomial Tree Model of Mathematical Finance.- 24. Special Topic: Optimal Stopping Rules.- 25. Special Topic: A Comprehensive Renewal Theory for General Random Walks.- 26. Special Topic: Ruin Problems in Insurance.- 27. Special Topic: Fractional Brownian Motion and/or Trends: The Hurst Effect.- 28. Special Topic: Incompressible Navier–Stokes Equations and the LeJan–Sznitman Cascade.- References.- Related Textbooks and Monographs.- Symbol Definition List.- Name Index.- Index.