Introduction to Stochastic Processes - Rilegato

Lawler, Gregory F.

 
9780412995118: Introduction to Stochastic Processes
Rilegato
ISBN 10: 0412995115 ISBN 13: 9780412995118
Casa editrice: Chapman and Hall/CRC, 1995

Sinossi

This concise, informal introduction to stochastic processes evolving with time was designed to meet the needs of graduate students not only in mathematics and statistics, but in the many fields in which the concepts presented are important, including computer science, economics, business, biological science, psychology, and engineering.

With emphasis on fundamental mathematical ideas rather than proofs or detailed applications, the treatment introduces the following topics:

  • Markov chains, with focus on the relationship between the convergence to equilibrium and the size of the eigenvalues of the stochastic matrix
  • Infinite state space, including the ideas of transience, null recurrence and positive recurrence
  • The three main types of continual time Markov chains and optimal stopping of Markov chains
  • Martingales, including conditional expectation, the optional sampling theorem, and the martingale convergence theorem
  • Renewal process and reversible Markov chains
  • Brownian motion, both multidimensional and one-dimensional

    Introduction to Stochastic Processes is ideal for a first course in stochastic processes without measure theory, requiring only a calculus-based undergraduate probability course and a course in linear algebra.

    • Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

    Contenuti

    PRELIMINARIES
    Introduction
    Linear Differential Equations
    Linear Difference Equations
    FINITE MARKOV CHAINS
    Definitions and Examples
    Long-Range Behavior and Invariant Probability
    Classification of States
    Return Times
    Transient States
    Examples
    COUNTABLE MARKOV CHAINS
    Introduction
    Recurrence and Transience
    Positive Recurrence and Null Recurrence
    Branching Process
    CONTINUOUS-TIME MARKOV CHAINS
    Poisson Process
    Finite State Space
    Birth-and-Death Processes
    General Case
    OPTIMAL STOPPING
    Optimal Stopping of Markov Chains
    Optimal Stopping with Cost
    Optimal Stopping with Discounting
    MARTINGALES
    Conditional Expectation
    Definition and Examples
    Optional Sampling theorem
    Uniform Integrability
    Martingale Convergence Theorem
    RENEWAL PROCESSES
    Introduction
    Renewal Equation
    Discrete Renewal Processes
    M/G/1 and B/M/1 Queues
    REVERSIBLE MARKOV CHAINS
    Reversible Processes
    Convergence to Equilibrium
    Markov Chain Algorithms
    A Criterion for Recurrence
    BROWNIAN MOTION
    Introduction
    Markov Property
    Zero Set of Brownian Motion
    Brownian Motion in Several Dimensions
    Recurrence and Transience
    Fractal Nature of Brownian Motion
    Brownian Motion with Drift
    STOCHASTIC INTEGRATION
    Integration with Respect to Random walk
    Integration with Respect to Brownian Motion
    Ito's Formula
    Simulation
    INDEX

    Product Description

    Book by Lawler Gregory F

    Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

    Editore
    Chapman and Hall/CRC
    Data di pubblicazione
    1995
    Lingua
    Inglese
    ISBN 10 
    0412995115
    ISBN 13 
    9780412995118
    Rilegatura
    Copertina rigida
    Numero edizione
    1
    Numero di pagine
    192
    Contatto del produttore
    non disponibile
    Persona responsabile
    non disponibile