Essentials of Stochastic process

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1、1EssentialsofStochasticProcessesRickDurrettVersionBetaofthe2ndEditionAugust21,2010Copyright2010,Allrightsreserved.2Contents1MarkovChains31.1DefinitionsandExamples...............31.2MultistepTransitionProbabilities...........131.3ClassificationofStates......

2、...........181.4StationaryDistributions................271.5LimitBehavior.....................331.6SpecialExamples....................421.6.1Doublystochasticchains............421.6.2Detailedbalancecondition...........451.6.3Reversibility..................

3、.511.7ProofsoftheTheorems1.7–1.11............531.8Exitdistributions....................601.9Exittimes........................681.10InfiniteStateSpaces*..................751.11ChapterSummary...................831.12Exercises.........................872Poiss

4、onProcesses1072.1ExponentialDistribution................1072.2DefiningthePoissonProcess..............1122.3CompoundPoissonProcesses.............1202.4Transformations.....................1232.4.1Thinning.....................1232.4.2Superposition............

5、......1252.4.3Conditioning..................1262.5Exercises.........................1283CONTENTS13Renewalprocesses1373.1Lawsoflargenumbers.................1373.2ApplicationstoQueueingTheory...........1463.2.1GI/G/1queue..................1463.2.2M/G/1queue

6、..................1503.3AgeandResidualLife.................1533.3.1Discretecase..................1533.3.2Age.......................1553.3.3Generalcase...................1573.4Renewalequations...................1623.5Exercises........................1674Ma

7、rkovChainsinContinuousTime1714.1DefinitionsandExamples...............1714.2ComputingtheTransitionProbability.........1794.3LimitingBehavior....................1854.4MarkovianQueues...................1924.5QueueingNetworks...................1994.6ClosedQueu

8、eingNetworks...............2094.7Exercises.........................2155Martingales2255.1ConditionalExpectation................2255.2ExamplesofMartingales................2285.3PropertiesofMartingales................2