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Schilling, René L.

Martingale und Prozesse

[Processes and Martingales]

Series:De Gruyter Studium

    19,95 € / $22.99 / £18.00*

    Paperback
    Publication Date:
    May 2018
    ISBN
    978-3-11-035067-8
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    Overview

    Aims and Scope

    This is the third volume of the series "Moderne Stochastik" (Modern Stochastics). As a follow-up to the volume "Wahrscheinlichkeit" (Probability Theory) it gives an intrdouction to dynamical aspects of probability theory using stochastic processes in discrete time. The first part of the book covers discrete martingales - their convergenc behaviour, optional sampling and stopping, uniform integrability and essential martingale inequalities. The power of martingale techniques is illustrated in the chapters on applications of martingales in classical probability and on the Burkholder-Davis-Gundy inequalities. The second half of the book treats random walks on Zd and Rd, their fluctuation behaviour, recurrence and transience. The last two chapters give a brief introduction to probabilistic potential theory and an outlook of further developments: Brownian motion and Donsker's invariance principle

    Contents
    Fair Play
    Conditional Expectation
    Martingale
    Stopping and Localizing
    Martingale Convergence
    L2-Martingales
    Uniformly Integrable Martingales
    Some Classical Results of Probability
    Elementary Inequalities for Martingales
    The Burkholder–Davis–Gundy Inequalities
    Random Walks on ℤd – the first steps
    Fluctuations of Simple Random Walks on Z
    Recurrence and Transience of General Random Walks
    Random Walks and Analysis
    Donsker's Invariance Principle and Brownian Motion

    Details

    24.0 x 17.0 cm
    x, 196 pages
    24 Fig.
    Language:
    German
    Type of Publication:
    Textbook
    Readership:
    Students of mathematics, biology and economics, instructors, libraries

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    René L. Schilling, Technische Universität Dresden, Germany.

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