Séminaire de Probabilités XLIII PDF
Preview Séminaire de Probabilités XLIII
Lecture Notes in Mathematics 2006 Editors: J.-M.Morel,Cachan F.Takens,Groningen B.Teissier,Paris Catherine Donati-Martin (cid:2) Antoine Lejay Alain Rouault (Eds.) Séminaire de Probabilités XLIII ABC Editors CatherineDonati-Martin AlainRouault LaboratoiredeProbabilitésetModèles LMV Aléatoires UniversitédeVersailles-Saint-Quentin UniversitéPierreetMarieCurie 45avnuedeEtats-Unis Boitecourrier188 78035VersaillesCedex,France 4,placeJussieu [email protected] 75252ParisCedex05,France [email protected] AntoineLejay IECN Campusscientifique BP70239 54506Vandoeuvre-lès-NancyCEDEX France [email protected] ISBN:978-3-642-15216-0 e-ISBN:978-3-642-15217-7 DOI:10.1007/978-3-642-15217-7 SpringerHeidelbergDordrechtLondonNewYork LectureNotesinMathematicsISSNprintedition:0075-8434 ISSNelectronicedition:1617-9692 LibraryofCongressControlNumber:2010937110 Mathematics Subject Classification (2010): 60Gxx, 60Hxx, 60Jxx, 60Kxx, 60G22, 60G44, 60H35, 46L54 (cid:2)c Springer-VerlagBerlinHeidelberg2011 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations areliabletoprosecutionundertheGermanCopyrightLaw. Theuseofgeneral descriptive names,registered names,trademarks, etc. inthis publication does not imply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotective lawsandregulationsandthereforefreeforgeneraluse. Coverdesign:SPiPublisherServices Printedonacid-freepaper springer.com Preface Theseriesofadvancedcourses,initiatedinSéminairedeProbabilitésXXXIII,con- tinueswithacourseofJeanPicardontherepresentationformulaeforthefractional Brownian motion.The rest of the volume coversa wide range of themes, such as stochastic calculusand stochastic differentialequations, stochastic differentialge- ometry,filtrations,analysisonWienerspace,randommatricesandfreeprobability, mathematicalfinance.SomeofthecontributionswerepresentedattheJournéesde ProbabilitésheldinPoitiersinJune2009. TheSéminairehasnowanewwebsiteattheURL http://portail.mathdoc.fr/SemProba/ ThiswebsiteishostedbytheCelluleMathDocfundedbothbytheCNRSandthe UniversitéJosephFourierinGrenoble,France.WethanktheteamoftheInstitutde RechercheMathématiquesAvancées(IRMA)inStrasbourgforthemaintenanceof theformerwebsite. With the new web site also comes a new multicriteria research tool which im- proves the previous one. This tool has been developped by the Cellule MathDoc (LaurentGuillopé, Elizabeth Cherhal and Claude Goutorbe). The enormouswork of indexing and commenting was started by Paul-André Meyer in 1995 with the helpofothereditors,withanimportantcontributionfromMichelÉmery(whoper- formed the supervision of all the work) and Marc Yor. The database covers now thecontentsofvolumesItoXL.We expecttocompletetheworksooninorderto providesomeeasywaytoexploitfullythecontentoftheSéminaire. We remindyouthattheCellule MathDoc also hostsdigitizedarticlesofmany scientific journalswithin the NUMDAM project. All the articles of the Seminaire fromVolumeI in 1967to VolumeXXXVI in 2002are freelyaccessible fromthis website http://www.numdam.org/numdam-bin/feuilleter?j=SPS Finally, the Rédaction of the Séminaire is modified: Christophe Stricker and Michel Émery retired from our team after Séminaire XLII was completed. Both contributed early and continuously as authors and accepted to invest energy and timeasRédacteurs.MichelÉmerywasamemberoftheboardsincevolumeXXIX. v vi Preface Duringalltheseyears,theSéminairebenefitedfromhisdemandingqualityrequire- ments, be it on mathematics and on style. His meticulous reading of articles was sometimessupplementedbyarewritingsuggestingnotablyelegantphrasesinstead ofbasicEnglish. Whilepreparingthisvolume,weheardthesadnewsthatLesterDubins,professor emeritusatBerkeleyUniversity,passedaway.Fromtheearlydays,severaltalentu- ous mathematiciansfrom variouscountrieshave contributedto the Séminaire and Dubinswasoneofthem. C.Donati-Martin A.Lejay A.Rouault Contents SPECIALIZEDCOURSE RepresentationFormulaefortheFractionalBrownianMotion .............. 3 JeanPicard OTHERCONTRIBUTIONS HorizontalDiffusioninC1PathSpace........................................... 73 MarcArnaudon,KoléhèAbdoulayeCoulibaly, andAntonThalmaier AStochasticCalculusProofoftheCLTfortheL2 Modulus ofContinuityofLocalTime....................................................... 95 JayRosen On a Zero-One Law for the Norm Process of Transient RandomWalk ......................................................................105 AyakoMatsumotoandKoujiYano OnStandardnessandI-cosiness..................................................127 StéphaneLaurent OnIsomorphicProbabilitySpaces...............................................187 ClaudeDellacherie CylindricalWienerProcesses.....................................................191 MarkusRiedle ARemarkonthe1=H-VariationoftheFractionalBrownian Motion...............................................................................215 MaurizioPratelli vii viii Contents SimulationofaLocalTimeFractionalStableMotion.........................221 MatthieuMarouby Convergence at First and Second Order ofSomeApproximationsofStochasticIntegrals ...............................241 BlandineBérardBergeryandPierreVallois ConvergenceofMulti-DimensionalQuantizedSDE’s .........................269 GillesPagèsandAfefSellami AsymptoticCramér’sTheoremandAnalysisonWienerSpace..............309 CiprianA.Tudor MomentsoftheGaussianChaos .................................................327 JosephLehec TheLentParticleMethodforMarkedPointProcesses........................341 NicolasBouleau EwensMeasuresonCompactGroupsandHypergeometric Kernels ..............................................................................351 PaulBourgade,AshkanNikeghbali,andAlainRouault DiscreteApproximationoftheFreeFockSpace................................379 StéphaneAttalandIonNechita ConvergenceintheSemimartingaleTopologyandConstrained Portfolios............................................................................395 ChristophCzichowsky,NicholasWestray,andHarryZheng Closedness in the Semimartingale Topology for Spaces ofStochasticIntegralswithConstrainedIntegrands ..........................413 ChristophCzichowskyandMartinSchweizer OnMartingaleswithGivenMarginalsandtheScalingProperty ............437 DavidBakerandMarcYor A Sequence of Albin Type Continuous Martingales withBrownianMarginalsandScaling...........................................441 DavidBaker,CatherineDonati-Martin,andMarcYor ConstructingSelf-SimilarMartingalesviaTwoSkorokhod Embeddings.........................................................................451 Francis Hirsch, Christophe Profeta, Bernard Roynette, andMarcYor Contributors Marc Arnaudon Laboratoire de Mathématiques et Applications CNRS: UMR6086,UniversitédePoitiers, Téléport2 - BP 30179,86962Futuroscope ChasseneuilCedex,France,[email protected] StéphaneAttal UniversitédeLyon,UniversitédeLyon1,InstitutCamilleJordan, CNRS UMR 5208,43, Boulevarddu 11 novembre1918,69622Villeurbanne Cedex,France,[email protected] DavidBaker LaboratoiredeProbabilitésetModèlesAléatoires,UniversitéPierre etMarieCurie,UniversitéParis06andCNRS,UMR7599,4,PlaceJussieu,75252 ParisCedex05,France,[email protected] Blandine BérardBergery Institutde MathématiquesElie Cartan, Université HenriPoincaréNancyI,B.P.239,54506Vandoeuvre-lès-NancyCedex,France, [email protected] NicolasBouleau EcoledesPontsParisTech,Paris,France,[email protected] PaulBourgade InstitutTelecom&UniversitéParis6,46rueBarrault, 75634ParisCedex13,France,[email protected] KoléhèAbdoulaye Coulibaly Laboratoirede MathématiquesetApplications CNRS: UMR 6086, Université de Poitiers, Téléport 2 - BP 30179, 86962 FuturoscopeChasseneuilCedex,France, [email protected] and UnitédeRechercheenMathématiques,FSTC,UniversitéduLuxembourg, 6,rue RichardCoudenhove-Kalergi,1359Luxembourg,Grand-DuchyofLuxembourg, [email protected] ChristophCzichowsky DepartmentofMathematics,ETHZurich,Rämistrasse 101,CH-8092Zurich,Switzerland,[email protected] ClaudeDellacherie LaboratoireRaphaëlSalem,C.N.R.S.etUniversitédeRouen Avenuedel’Université, BP.12,76801Saint-Étienne-du-Rouvray,France,claude. [email protected] ix x Contributors CatherineDonati-Martin LaboratoiredeProbabilitésetModèlesAléatoires, UniversitéPierreetMarieCurieUniversitéParis06andCNRS, UMR7599,4, PlaceJussieu,75252ParisCedex05,France,[email protected] FrancisHirsch Laboratoired’AnalyseetProbabilités,Universitéd’Evry- Vald’Essonne,BoulevardF.Mitterrand,91025EvryCedex,France, [email protected] StéphaneLaurent UniversitécatholiquedeLouvain,Louvain-la-Neuve,Belgium Present Address: Université de Strasbourg,IRMA, UMR 7501, 7 rue René- Descartes, 67084StrasbourgCedex,France, [email protected] JosephLehec CEREMADE (UMR CNRS 7534),UniversitéParis-Dauphine, PlacedumaréchaldeLattredeTassigny,75016Paris,France, [email protected] Matthieu Marouby Institut de Mathématiquesde Toulouse, Université Paul Sabatier,31062Toulouse,France,[email protected] AyakoMatsumoto T&DFinancialLifeInsuranceCompany,Japan IonNechita UniversitédeLyon,UniversitédeLyon1,InstitutCamilleJordan, CNRS UMR 5208,43, Boulevarddu 11 novembre1918,69622Villeurbanne Cedex,France,[email protected] Ashkan Nikeghbali Institut für Mathematik,UniversitätZürich,Winterthur- erstrasse190,CH-8057Zürich,Switzerland, [email protected] GillesPagès Laboratoirede ProbabilitésetModèlesAléatoires,Universitéde Paris6,Case188,4pl.Jussieu,75252ParisCedex5,France,[email protected] JeanPicard Laboratoirede Mathématiques,ClermontUniversité,Université BlaisePascalandCNRSUMR6620,BP10448,63000Clermont-Ferrand,France, [email protected] MaurizioPratelli DipartimentodiMatematica,LargoB.Pontecorvo5, 56127Pisa,Italy,[email protected] Christophe Profeta InstitutElie Cartan,UniversitéHenriPoincaré,B.P. 239, 54506Vandœuvre-lès-NancyCedex,France, [email protected] Markus Riedle School of Mathematics, The University of Manchester, ManchesterM139PL,UK,[email protected] JayRosen DepartmentofMathematics,CollegeofStatenIsland,CUNY, StatenIsland,NY10314,USA,[email protected] AlainRouault UniversitéVersailles-SaintQuentin,LMV,BâtimentFermat, 45avenuedesEtats-Unis,78035VersaillesCedex,France, [email protected]
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