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1、AnIntroductiontoStochasticProcessesinPhysicsAnIntroductiontoStochasticProcessesinPhysicsContaining“OntheTheoryofBrownianMotion”byPaulLangevin,translatedbyAnthonyGythielDONS.LEMONSTHEJOHNSHOPKINSUNIVERSITYPRESSBALTIMOREANDLONDONCopyrightc2002TheJohnsHopkinsUniv
2、ersityPressAllrightsreserved.Published2002PrintedintheUnitedStatesofAmericaonacid-freepaper987654321TheJohnsHopkinsUniversityPress2715NorthCharlesStreetBaltimore,Maryland21218-4363www.press.jhu.eduLibraryofCongressCataloging-in-PublicationDataLemons,DonS.(DonSt
3、ephen),1949–Anintroductiontostochasticprocessesinphysics/byDonS.Lemonsp.cm.Includesbibliographicalreferencesandindex.ISBN0-8018-6866-1(alk.paper)–ISBN0-8018-6867-X(pbk.:alk.paper)1.Stochasticprocesses.2.Mathematicalphysics.I.Langevin,Paul,1872–1946.II.Title.QC2
4、0.7.S8L452001530.15923–dc212001046459AcatalogrecordforthisbookisavailablefromtheBritishLibraryForAllison,Nathan,andMicahContentsPrefaceandAcknowledgmentsxiChapter1–RandomVariables11.1RandomandSureVariables11.2AssigningProbabilities21.3TheMeaningofIndependence4
5、Problems:1.1.CoinFlipping,1.2.IndependentFailureModes5Chapter2–ExpectedValues72.1Moments72.2MeanSumTheorem92.3VarianceSumTheorem102.4CombiningMeasurements12Problems:2.1.DiceParameters,2.2.PerfectLinearCorrelation,2.3.ResistorsinSeries,2.4.DensityFluctuations14C
6、hapter3–RandomSteps173.1BrownianMotionDescribed173.2BrownianMotionModeled183.3CritiqueandProspect19Problems:3.1.Two-DimensionalRandomWalk,3.2.RandomWalkwithHesitation,3.3.MultistepWalk,3.4.Autocorrelation,3.5.FrequencyofHeads20Chapter4–ContinuousRandomVariables
7、234.1ProbabilityDensities234.2Uniform,Normal,andCauchyDensities244.3Moment-GeneratingFunctions27Problems:4.1.Single-SlitDiffraction,4.2.MomentsofaNormal,4.3.ExponentialRandomVariable,4.4.PoissonRandomVariable29Chapter5–NormalVariableTheorems335.1NormalLinearTra
8、nsformTheorem335.2NormalSumTheorem345.3JointlyNormalVariables35viiiCONTENTS5.4CentralLimitTheorem36Problems:5.1.UniformLinearTransform,5.2.AddingUniformVariables,5.3.Depende
