Document Type
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BL
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Record Number
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667843
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Doc. No
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dltt
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Main Entry
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Kirkwood, James R.
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Title & Author
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Markov processes /\ James R. Kirkwood
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Series Statement
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Advances in applied mathematics
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Page. NO
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xii, 327 pages :: illustrations ;; 24 cm
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ISBN
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9781482240733
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: 1482240734
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Bibliographies/Indexes
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Includes bibliography (page 321) and index
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Contents
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Review of probability. Short history ; Review of basic probability definitions ; Some common probability distributions ; Properties of a probability distribution ; Properties of the expected value ; Expected value of a random variable with common distributions ; Generating functions moment generating functions -- Discrete-time, finite-state Markov chains. Notation ; Transition matrices ; Directed graphs: examples of Markov chains ; Random walk with reflecting boundaries ; Gambler's ruin ; Ehrenfest model ; Central problem of Markov chains ; Condition to ensure a unique equilibrium state ; Finding the equilibrium state ; Transient and recurrent states ; Indicator functions ; Perron-frobenius theorem ; Absorbing Markov chains ; Mean first passage time ; Mean recurrence time and the equilibrium state ; Fundamental matrix for regular Markov chains ; Dividing a Markov chain into equivalence classes ; Periodic Markov chains ; Reducible Markov chains -- Discrete-time, finite-state Markov chains. Renewal processes ; Delayed renewal processes ; Equilibrium state for countable Markov chains ; Physical interpretation of the equilibrium state ; Null recurrent versus positive recurrent states ; Difference equations ; Branching processes ; Random walk in
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Exponential distribution and poisson process. Continuous random variables ; Cumulative distribution function (continuous case) ; Exponential distribution ; o(h) functions ; Exponential distribution as a model for arrivals ; Memoryless random variables ; Poisson process ; Poisson processes with occurrences of two types -- Continuous-time Markov chains. Generators of continuous Markov chains: the Kolmogorov ; Forward and backward equations ; Connection between the steady state of a continuous Markov ; Chain and the steady state of the embedded matrix ; Explosions ; Birth and birth-death processes ; Birth and death processes ; Queuing models ; Detailed balance equations -- Reversible Markov chains. Random walks on weighted graphs ; Discrete-time birth-death process as a reversible Markov chain ; Continuous-time reversible Markov chains
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Subject
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Markov processes
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Subject
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Markov processes
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LC Classification
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QA274.7.K57 2015
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