Random walk, Brownian motion, and Ma...
Bhattacharya, Rabi.

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  • Random walk, Brownian motion, and Martingales
  • Record Type: Electronic resources : Monograph/item
    Title/Author: Random walk, Brownian motion, and Martingales/ by Rabi Bhattacharya, Edward C. Waymire.
    Author: Bhattacharya, Rabi.
    other author: Waymire, Edward C.
    Published: Cham :Springer International Publishing : : 2021.,
    Description: xv, 396 p. :ill., digital ;25 cm.
    [NT 15003449]: 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. Bienyame-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 Bienyame-Galton-Watson Simple Branching Processes -- 15. Stochastic Calculus for Point Processes and a Martingale Characterization of the Poisson Process -- 16. First Passage Time Distributions for Brownian 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: Bienyame-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.
    Contained By: Springer Nature eBook
    Subject: Random walks (Mathematics) -
    Online resource: https://doi.org/10.1007/978-3-030-78939-8
    ISBN: 9783030789398
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W9409572 電子資源 11.線上閱覽_V 電子書 EB QA274.73 .B53 2021 一般使用(Normal) On shelf 0
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