Surveys in Stochastic Processes

264 Pages·2011·1.807 MB·English

by  Blath J., et al. (eds.)

EMS Series of Congress Reports
EMS Congress Reportspublishes volumes originating from conferences or seminars focusing on any field
of pure or applied mathematics.The individual volumes include an introduction into their subject and
review of the contributions in this context.Articles are required to undergo a refereeing process and are
accepted only if they contain a survey or significant results not published elsewhere in the literature.
Previously published:
Trends in Representation Theory of Algebras and Related Topics,Andrzej Skowron´ski (ed.)
K-Theory and Noncommutative Geometry,Guillermo Cortiñaset al. (eds.)
Classification of Algebraic Varieties,Carel Faber, Gerard van der Geer and Eduard Looijenga (eds.)
Surveys
in Stochastic
Processes
Jochen Blath
Peter Imkeller
Sylvie Rœlly
Editors
Editors:
Jochen Blath Peter Imkeller Sylvie Rœlly
Institut für Mathematik Institut für Mathematik Institut für Mathematik der
Technische Universität Berlin Humboldt-Universität zu Berlin Universität Potsdam
Straße des 17.Juni 136 Unter den Linden 6 Am Neuen Palais,10
10623 Berlin 10099 Berlin 14469 Potsdam
Germany Germany Germany
[email protected] [email protected] [email protected]
2010 Mathematics Subject Classification:Primary:60-06,Secondary 60Gxx,60Jxx
Key words:Stochastic processes,stochastic finance,stochastic analysis,statistical physics,stochastic
differential equations
ISBN 978-3-03719-072-2
The Swiss National Library lists this publication in The Swiss Book,the Swiss national bibliography,
and the detailed bibliographic data are available on the Internet at http://www.helveticat.ch.
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is concerned,specifically the rights of translation,reprinting,re-use of illustrations,recitation,
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© 2011 European Mathematical Society
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Preface
In this volume many of the plenary lecturers of the 33rd Conference on Stochastic
ProcessesandTheirApplicationspresenttheirpersonalsnapshotsofrecentimportant
developments that they have been involved in within the area of stochastic processes
andtheirapplications. Thisreflectstheidealeadingustocomposethiscongressreport:
topresentacollectionofsurveytypearticlesthatofferaglimpseofthestate-of-the-art
inmanyofthepromisingandthrivingfieldsoftheareaofstochasticprocessesandtheir
applicationsatthemomentthisSPAconferencewasheld.
One of our hopes is that this collection may help young scientists in setting up
researchgoalsinthewidescopeoffieldsrepresentedinthisvolume.
Toourknowledge,thisisthefirsttimethatproceedingsofanSPAconferencehas
beenpublished. TheideaforthisvolumegrewamongtheorganizersinSpring2009,
andafterameetingwithProfessorMartaSanz-SoléfromtheBernoulliSocietyinBerlin
anduponapprovalbyboththeCCSP1 andthepublishingcommitteeoftheBernoulli
Societywedecidedtogoaheadwithit.Asaparticularlywelcomeeffectofthisvolume
wecouldimaginestartingatraditionforforthcomingSPAevents.
We wish to thank all contributing plenary speakers, anonymous referees and the
EMSpublishinghouseformakingthisvolumepossible.
Onbehalfofthe33rdSPAorganizingcommittee: Enjoyreading!
BerlinandPotsdam,June2011 JochenBlath
PeterImkeller
SylvieRœlly
1‘Committeeforconferencesonstochasticprocesses’oftheBernoulliSociety.

Contents
Preface .....................................................................v
The33rdSPAConference2009...............................................ix
PlenaryLectures ...........................................................xii
CommitteesoftheConference...............................................xiv
ListofDonors..............................................................xv
Optimalswitching,systemsofreflectedBSDEsandsystemsofvariational
inequalitieswithinter-connectedobstacles
bySaïdHamadène...........................................................1
TheCOGARCH:areview,withnewsonoptionpricingandstatisticalinference
byClaudiaKlüppelberg,RossMallerandAlexanderSzimayer .................. 29
Somepropertiesofquasi-stationarydistributionsforfiniteMarkovchains
byServetMartínezandJaimeSanMartín.....................................59
TheparabolicAndersonmodelwithheavy-tailedpotential
byPeterMörters............................................................67
Fromexplorationpathstomassexcursions–variationsonathemeofRay
andKnight
byEtiennePardouxandAntonWakolbinger....................................87
Gaussianapproximationoffunctionals: MalliavincalculusandStein’smethod
byGesineReinert..........................................................107
MergingandstabilityfortimeinhomogeneousfiniteMarkovchains
byLaurentSaloff-CosteandJessicaZúñiga .................................. 127
Somemathematicalaspectsofmarketimpactmodeling
byAlexanderSchiedandAllaSlynko.........................................153
Theself-avoidingwalk: Abriefsurvey
byGordonSlade...........................................................181
viii Contents
Lp-independenceofgrowthboundsofFeynman–Kacsemigroups
byMasayoshiTakeda ......................................................201
Somerecentprogressonfunctionalinequalitiesandapplications
byFeng-YuWang..........................................................227
ListofContributors ........................................................247
The 33rd SPA Conference 2009
The33rdConferenceonStochasticProcessesandTheirApplications(SPA)washeld
inBerlinfromJuly27throughJuly31,2009,withmorethan600participantsfrom49
countries1.
TheconferencecontinuedasuccessfulseriesofSPAconferencesinthisprospering
fieldofmathematics,whichisbothreflectedinthegrowingnumberandinternationality
of participants, as well as in the size of the program and the recognition for the field
withinmathematics.
One indication of this might be seen in the felicitous fact that one of the plenary
speakers,ProfessorStanislavSmirnovfromGeneva,wasawardedwithaFieldsMedal
in2010.
The main aim behind the selection of the 20 plenary lectures at this conference
was to give an overview of recent developments in the rich current active research
fields in Stochastic Processes and TheirApplications, in particular aimed at younger
participants. They were also chosen to reflect the variety of the current probability
communitywithrespecttoresearchtopics,scientificageanddiversitywithrespectto
geographyandgender. Wethinkthatthishasworkedverywell,andhenceourthanks
gotothemembersofthescientificcommittee(seebelow).
We particularly encouraged young researchers and researchers from developing
countriestoparticipate. Morethan300talksand40posterpresentations,manyofthem
byyoungparticipants,reflectedthevibrancyofthefieldandprovidedaninternational
forumforscientificandculturalexchange.
One further major aim of this conference was to make the stochastic processes
community feel at home. Hence, we put particular emphasis on the social and public
program of the conference, a few highlights of which we would like to report about
brieflyhere.
During a reception in the ‘Lichthof’ofTU Berlin on the first evening of the con-
ference, following a welcome address by Staatssekretär Dr. Hans-Gerhard Husung
on behalf of the Senate of the State of Berlin, Professor Alice Guionnet from Lyon
was announced as winner of the 2009 Loève prize. The elegant musical background
throughoutthereceptionwasprovidedbyaclassicaltriowithdirectlinkstotheproba-
bilitycommunity,namelyAliceAdenot-Meyer2 (Mezzo-Soprano),ThérèseDourdent
(Piano)andProfessorSylvieRœlly(Cello). ProfessorRuthWilliamsfromSanDiego
provided a personal obituary, remembering the recently deceased Professor Kai Lai
Chung(1917–2009).
On the second evening, Professor Marc Wouts from Paris was awarded with the
Itô-Prize. The sad occasion of the recent passing away of one of the most influential
probabilists,ProfessorKiyoshiItô(1915–2008),wasrememberedbyatouchingand
1Detailedconferenceinformationcanbefoundatwww.math.tu-berlin.de/SPA2009
2AliceAdenot-MeyerisadaughterofPaul-AndréMeyer
x The33rdSPAConference2009
charming presentation of his life and work by Professor Masatoshi Fukushima from
Osaka.
A large part of the evening was devoted to the work and tragic life of the Berlin-
bornmathematicianWolfgangDöblin. WolfgangDöblin(1915–1940)wasthesecond
sonofthefamousJewish-GermannovelistAlfredDöblin(‘BerlinAlexanderplatz’),an
eminentfigureinGermanintellectuallifeduringtheWeimarerRepublik. In1933,his
familyescapedtheNazistoParis,whereWolfgangbecameaFrenchcitizenandstudied
probability at the Institut Henri Poincaré. He wrote a brilliant dissertation under the
supervisionofMauriceFréchetin1938. Oneyearlater,WolfgangDöblinwasdrafted
forFrenchmilitaryservice. InMay1940,facingimminentcapturebytheWehrmacht,
he took his own life in Housseras (Vosges, France). Before, however, he was able to
mail his last mathematical manuscript “Sur l’équation de Kolmogoroff” in a sealed
envelopetotheAcadémiedesSciences,whichremainedunopenedfor60years. Ithas
only recently been discovered and investigated by Bernard Bru and MarcYor, and it
turnedoutthatitcontainsspectacularresults,inparticularrelatedtotheworkofItô.
ThescreeningofarecentdocumentaryonWolfgangDöblinslifeandmathematical
legacyinthepresenceofthefilmmakersAgnesHandwerkandHarryWillemsfollowed
anintroductiontohismathematicalworkandlifebyProfessorHansFöllmer.
Figure1. DuringtheMondayreceptionatTULichthof.
The success of this conference would not have been possible without the tireless
commitmentofmanypeople. First, wewishtothankallplenary, invitedsessionand
contributedsessionspeakersandtheposterpresentersfortheirscientificcontributions.
WefurtherwishtothankthescientificcommitteeandtherepresentativesoftheBernoulli