1st Edition

Martingales and Markov Chains Solved Exercises and Elements of Theory

    200 Pages 10 B/W Illustrations
    by Chapman & Hall

    200 Pages
    by Chapman & Hall

    A thorough grounding in Markov chains and martingales is essential in dealing with many problems in applied probability, and is a gateway to the more complex situations encountered in the study of stochastic processes. Exercises are a fundamental and valuable training tool that deepen students' understanding of theoretical principles and prepare them to tackle real problems.

    In addition to a quick but thorough exposition of the theory, Martingales and Markov Chains: Solved Exercises and Elements of Theory presents, more than 100 exercises related to martingales and Markov chains with a countable state space, each with a full and detailed solution. The authors begin with a review of the basic notions of conditional expectations and stochastic processes, then set the stage for each set of exercises by recalling the relevant elements of the theory. The exercises range in difficulty from the elementary, requiring use of the basic theory, to the more advanced, which challenge the reader's initiative. Each section also contains a set of problems that open the door to specific applications.

    Designed for senior undergraduate- and graduate level students, this text goes well beyond merely offering hints for solving the exercises, but it is much more than just a solutions manual. Within its solutions, it provides frequent references to the relevant theory, proposes alternative ways of approaching the problem, and discusses and compares the arguments involved.

    CONDITIONAL EXPECTATIONS
    Introduction
    Definition and First Properties
    Conditional Expectations and Conditional Laws
    Exercises
    Solutions
    STOCHASTIC PROCESSES
    General Facts
    Stopping Times
    Exercises
    Solutions
    MARTINGALES
    First Definitions
    First Properties
    The Stopping Theorem
    Maximal Inequalities
    Square Integral Martingales
    Convergence Theorems
    Regular Martingales
    Exercises
    Problems
    Solutions
    MARKOV CHAINS
    Transition Matrices, Markov Chains
    Construction and Existence
    Computations on the Canonical Chain
    Potential Operators
    Passage Problems
    Recurrence, Transience
    Recurrent Irreducible Chains
    Periodicity
    Exercises
    Problems
    Solutions
    REFERENCES
    INDEX

    Biography

    Baldi, Paolo