Introduction to Stochastic Processes

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CRC Press, 1995. 7. 1. - 192페이지
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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.
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    Preliminaries
    1
    Finite Markov Chains
    7
    Countable Markov Chains
    37
    ContinuousTime Markov Chains
    53
    Optimal Stopping
    73
    Martingales
    85
    Renewal Processes
    107
    Reversible Markov Chains
    129
    Brownian Motion
    143
    Stochastic Integration
    163
    Index
    175
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