Theory of Probability and Random Processes

Aone-yearcourseinprobabilitytheoryandthetheoryofrandomprocesses，taughtatPrincetonUniversitytoundergraduateandgraduatestudents，formsthecoreofthecontentofthisbookItisstructuredintwoparts：thefirstpartprovidingadetaileddiscussionofLebesgueintegration，Markovchains，randomwalks，lawsoflargenumbers，limittheorems，andtheirrelationtoRenormalizationGrouptheory.Thesecondpartincludesthetheoryofstationaryrandomprocesses，martingales，generalizedrandomprocesses，Brownianmotion，stochasticintegrals，andstochasticdifferentialequations.OnesectionisdevotedtothetheoryofGibbsrandomfields.Thismaterialisessentialtomanyundergraduateandgraduatecourses.Thebookcanalsoserveasareferenceforscientistsusingmodernprobabilitytheoryintheirresearch.