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1、MAT-51266StochasticProcessesRobertPiche′TampereUniversityofTechnology2010Stochastic(i.e.random)processesareprobabilisticmodelsofdatastreamssuchasspeech,audioandvideosignals,stockmarketprices,medicalinstrumentread-ings,aswellasofotherdynamicphenomenasuchasthemotionofaGPS
2、receiverorofthegroundduringanearthquake.Asolidunderstandingofthemathematicalbasisofthesemodelsisessentialforunderstandingphenomenaandprocessinginformationinmanybranchesofscienceandengineeringincludingphysics,com-munications,signalprocessing,automation,andstructuraldynam
3、ics.Thesecoursenotesintroducelineardiscrete-timemultivariatestochasticprocesstheorythatisneededforestimationandprediction.Itstartswithacompactre-viewofdiscreteandcontinuousrandomvariablesandrandomvectors.LinearmultivariateBayesianestimation(regression)isintroduced.There
4、followsapre-sentationofrandomsequences,includingdiscussionofconvergence,ergodicity,andpowerspectraldensity.Statespacemodelsoflinearsystemsareintroduced,andtheirresponsetotransientandstationaryrandominputsisstudied.Thebasic?lteringproblemisintroducedandtheKalmanalgorithm
5、isderived.Studentsareassumedtohaveknowledgeofbasicprobabilityandofmatrixalgebra.Additionalcoursematerials(includingexercisesandrecordedlectures)areavail-ableattheauthor’shomepagehttp://math.tut.fi/~piche/stochasticContents1RandomVariablesandVectors11.1Discreterandomvari
6、able......................11.1.1Speci?cation........................11.1.2Expectation.........................21.1.3Inequalities.........................3i1.1.4Characteristicfunction...................31.2Twodiscreterandomvariables...................41.2.1Speci?cation..
7、......................41.2.2Conditionaldistribution..................51.2.3Expectation.........................61.2.4Conditionalexpectation..................71.2.5Inequalities.........................71.2.6Characteristicfunction...................81.3Discreterandomvecto
8、r.......................81.3.1Speci?cation........................81.3.2Conditionaldistribution...............
