Séminaire de Probabilités XLIV PDF
Preview Séminaire de Probabilités XLIV
Lecture Notes in Mathematics 2046 Editors: J.-M.Morel,Cachan B.Teissier,Paris Forfurthervolumes: http://www.springer.com/series/304 • Catherine Donati-Martin Antoine Lejay (cid:2) Alain Rouault Editors Séminaire de Probabilités XLIV 123 Editors CatherineDonati-Martin AlainRouault UniversitédeVersailles-St-Quentin UniversitédeVersailles-St-Quentin Versailles Versailles France France AntoineLejay Nancy-Université,INRIA Vandoeuvre-lès-Nancy France ISBN978-3-642-27460-2 ISBN978-3-642-27461-9(eBook) DOI10.1007/978-3-642-27461-9 SpringerHeidelbergNewYorkDordrechtLondon LectureNotesinMathematicsISSNprintedition:0075-8434 ISSNelectronicedition:1617-9692 LibraryofCongressControlNumber:2012933110 MathematicsSubjectClassification(2010):60-XX,60JXX,60J60,60J10,60J65,60J55,46L54 (cid:2)c Springer-VerlagBerlinHeidelberg2012 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations areliabletoprosecutionundertherespectiveCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface As usual, some of the contributions to this 44th Séminaire de Probabilités were exposedduringtheJournéesdeProbabilitésheldinDijoninJune2010.Theother ones come from spontaneous submissions or were solicited by the editors. The traditional and historical themes of the Séminaire are present, such as stochastic calculus,localtimesandexcursionsandmartingales.Somesubjectsalreadylargely present in the previous volumes are stil here: free probability, rough paths, limit theoremsforgeneralprocesses(herefractionalBrownianmotionandpolymers)and largedeviations.Finally,thisvolumeexploresnewtopics,includingvariablelength Markovchains and peacoks. We hope that the whole volume is a good sample of the main streams of current research on probability and stochastic processes, in particularthoseactiveinFrance. WeremindthatthewebsiteoftheSéminaireis http://portail.mathdoc.fr/SemProba/ andthatallthearticlesoftheSéminairefromVolumeIin1967toVolumeXXXVI in2002arefreelyaccessiblefromthewebsite http://www.numdam.org/numdam-bin/feuilleter?j=SPS WethanktheCelluleMathDocforhostingallthesearticleswithintheNUMDAM project. CatherineDonati-Martin AntoineLejay AlainRouault v • Contents ContextTrees,VariableLengthMarkovChains andDynamicalSources.......................................................... 1 PeggyCénac,BrigitteChauvin,FrédéricPaccaut, andNicolasPouyanne MartingalePropertyofGeneralizedStochasticExponentials .............. 41 AleksandarMijatovic´,NikaNovak,andMikhailUrusov Some Classes of Proper Integrals and Generalized Ornstein–UhlenbeckProcesses................................................. 61 AndreasBasse-O’Connor,Svend-ErikGraversen, andJanPedersen Martingale Representations for Diffusion Processes andBackwardStochasticDifferentialEquations ............................ 75 ZhongminQianandJiangangYing QuadraticSemimartingaleBSDEs Under anExponential MomentsCondition.............................................................. 105 MarkusMochaandNicholasWestray TheDerivativeoftheIntersectionLocalTimeofBrownian MotionThroughWienerChaos ................................................ 141 GregMarkowsky OntheOccupationTimesofBrownianExcursions andBrownianLoops............................................................. 149 HaoWu DiscreteApproximationstoSolutionFlowsofTanaka’sSDE RelatedtoWalshBrownianMotion............................................ 167 HatemHajri vii viii Contents SpectralDistributionoftheFreeUnitaryBrownianMotion: AnotherApproach............................................................... 191 NizarDemniandTaoufikHmidi Another Failure in the Analogy Between Gaussian and SemicircleLaws .................................................................. 207 NathalieEisenbaum Global Solutions to Rough DifferentialEquations with UnboundedVectorFields ....................................................... 215 AntoineLejay AsymptoticBehaviorofOscillatoryFractionalProcesses................... 247 RenaudMartyandKnutSølna TimeInversionPropertyforRotationInvariantSelf-similar DiffusionProcesses............................................................... 271 JuhaVuolle-Apiala OnPeacocks:AGeneralIntroductiontoTwoArticles ...................... 279 Antoine-MarieBogso,ChristopheProfeta,andBernardRoynette SomeExamplesofPeacocksinaMarkovianSet-Up......................... 281 Antoine-MarieBogso,ChristopheProfeta,andBernardRoynette PeacocksObtainedbyNormalisation:Strong andVeryStrongPeacocks....................................................... 317 Antoine-MarieBogso,ChristopheProfeta,andBernardRoynette BranchingBrownianMotion:Almost SureGrowthAlong ScaledPaths....................................................................... 375 SimonC.HarrisandMatthewI.Roberts OntheDelocalizedPhaseoftheRandomPinningModel ................... 401 Jean-ChristopheMourrat Large Deviations for Gaussian Stationary Processes andSemi-ClassicalAnalysis .................................................... 409 BernardBercu,Jean-FrançoisBony,andVincentBruneau GirsanovTheoryUnderaFiniteEntropyCondition ........................ 429 ChristianLéonard ErratumtoSéminaireXXVII................................................... 467 MichelÉmeryandMarcYor ErratumtoSéminaireXXXV................................................... 469 MichelÉmeryandWalterSchachermayer Context Trees, Variable Length Markov Chains and Dynamical Sources PeggyCénac,BrigitteChauvin,FrédéricPaccaut,andNicolasPouyanne Abstract Infiniterandomsequencesofletterscanbeviewedasstochasticchainsor asstringsproducedbyasource,inthesenseofinformationtheory.Therelationship between Variable Length Markov Chains (VLMC) and probabilistic dynamical sourcesisstudied.We establisha probabilisticframeforcontexttreesandVLMC andwe provethatanyVLMCisadynamicalsourceforwhichwe explicitlybuild the mapping. On two examples, the “comb” and the “bamboo blossom”, we find a necessary and sufficient condition for the existence and the uniqueness of a stationaryprobabilitymeasureforthe VLMC.Thesetwo examplesaredetailedin orderto providetheassociated Dirichletseriesas wellasthe generatingfunctions ofwordoccurrences. P.Cénac((cid:2)) UniversitédeBourgogne,InstitutdeMathématiquesdeBourgogneIMBUMR5584CNRS, 9avenueAlainSavary-BP47870,21078DIJONCEDEX,Bourgogne,France e-mail:[email protected] B.Chauvin INRIARocquencourt,projectAlgorithms,DomainedeVoluceauB.P.105, 78153LeChesnayCEDEX,France LaboratoiredeMathématiquesdeVersailles,CNRS,UMR8100,UniversitédeVersailles- St-Quentin,45avenuedesEtats-Unis,78035VersaillesCEDEX,France e-mail:[email protected] F.Paccaut LAMFA,CNRS,UMR6140,UniversitédePicardieJulesVerne,33rueSaint-Leu, 80039Amiens,France e-mail:[email protected] N.Pouyanne LaboratoiredeMathématiquesdeVersailles,CNRS,UMR8100,UniversitédeVersailles- St-Quentin,45avenuedesEtats-Unis,78035VersaillesCEDEX,France e-mail:[email protected] C.Donati-Martinetal.(eds.),SéminairedeProbabilitésXLIV,LectureNotes 1 inMathematics2046,DOI10.1007/978-3-642-27461-9__1, ©Springer-VerlagBerlinHeidelberg2012
The list of books you might like
