stochastic-processes.pdf

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1、CONTENTSPage1Contents1Markovchains51.1SpecifyingandsimulatingaMarkovchain...................51.2TheMarkovproperty..............................81.3“It’salljustmatrixtheory”...........................91.4ThebasiclimittheoremofMarkovchains...................101.5Stationarydistributions...

2、..........................121.6Irreducibility,periodicity,andrecurrence....................151.7Anasideoncoupling...............................251.8ProofoftheBasicLimitTheorem.......................271.9ASLLNforMarkovchains...........................311.10Exercises.....................

3、................362MarkovChains:ExamplesandApplications432.1BranchingProcesses...............................432.2TimeReversibility................................462.3MoreonTimeReversibility:ATandemQueueModel............492.4TheMetropolismethod.............................532.5Simulate

4、dannealing...............................572.5.1Descriptionofthemethod........................582.5.2TheMainTheorem............................652.6ErgodicityConcepts...............................672.6.1TheErgodicCoefficient.........................682.6.2SufficientConditionsforWeakandStro

5、ngErgodicity........692.7ProofofMainTheoremofSimulatedAnnealing................712.8CardShuffling...................................732.8.1“Top-in-at-random”Shuffle.......................742.8.2ThresholdPhenomenon.........................742.8.3Arandomtimetoexactstationarity................

6、..762.8.4StrongStationaryTimes.........................772.8.5Proofofthresholdphenomenoninshuffling..............782.9Exercises.....................................81StochasticProcessesJ.Chang,February2,2007Page2CONTENTS3MRFsandHMMs873.1MRF’sonGraphsandHMM’s.........................873.2B

7、ayesianFramework...............................893.3Hammersley-CliffordTheorem..........................903.4LongrangedependenceintheIsingmodel...................973.5HiddenMarkovchains..............................993.5.1Descriptionofthemodel.........................1003.5.2How