Prokhorov and Contemporary Probability Theory: In Honor of Yuri V. Prokhorov

466 Pages·2013·5.86 MB·English

by  David J. Aldous (auth.)

Springer Proceedings in Mathematics
and Statistics
Volume 33
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Albert N. Shiryaev S. R. S. Varadhan
(cid:2)
Ernst L. Presman
Editors
Prokhorov and Contemporary
Probability Theory
In Honor of Yuri V. Prokhorov
123
Editors
AlbertN.Shiryaev ErnstL.Presman
SteklovMathematicalInstitute CentralEconomicsandMath.Institute
RussianAcademyofSciences RussianAcademyofSciences
Moscow Moscow
Russia Russia
S.R.S.Varadhan
CourantInstitute
NewYorkUniversity
NewYork
USA
ISSN2194-1009 ISSN2194-1017(electronic)
ISBN978-3-642-33548-8 ISBN978-3-642-33549-5(eBook)
DOI10.1007/978-3-642-33549-5
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2012954482
MathematicalSubjectClassification(2010):60xx,62xx,60Fxx,60Gxx,81S25
(cid:2)c Springer-VerlagBerlinHeidelberg2013
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Preface
This volume is dedicated to the prominent mathematician and leading expert on
probability theory and mathematical statistics Yuri Vasilyevich Prokhorov, who
celebratedhis80-thbirthdayon15December2009.
Itconsistsoftwoparts.Thefirstonecontainspaperswrittenbyhiscolleagues,
friendsandpupilswhoexpresstheirdeeprespectandsincerelylovetohimandhis
scientificactivity.
The second part contains two interviews with Yu.V. Prokhorov.The first inter-
viewwastakenbyFriedrichGo¨tzeandWillemR.vanZwetbetweenNovember13
and28,2006atBielefeldUniversity.
WedecidedtoreproducealsotheinterviewtakenbyLarrySheppandpublished
inStatisticalScience7(1992),123–130.
Moscow,Russia AlbertShiryev
NewYork,USA S.R.S.Varadhan
Moscow,Russia ErnstPresman
v
(cid:127)
Contents
YuriVasilyevichProkhorov................................................... xi
ListofPublicationsbyYu.V.Prokhorov..................................... xix
PartI ScientificPapers
WhenKnowingEarlyMatters:Gossip,PercolationandNash
Equilibria ....................................................................... 3
DavidJ.Aldous
AMathematicalModelofInvestmentIncentives........................... 29
VadimArkinandAlexanderSlastnikov
TheShapeofAsymptoticDependence....................................... 43
GuusBalkema,PaulEmbrechts,andNataliaNolde
LimitTheoremsforFunctionalsofHigherOrderDifferences
ofBrownianSemi-StationaryProcesses..................................... 69
Ole E. Barndorff-Nielsen,Jose´ ManuelCorcuera,and Mark
Podolskij
RetrievingInformationfromSubordination................................ 97
JeanBertoinandMarcYor
AsymptoticExpansionsforDistributionsofSums
ofIndependentRandomVectors ............................................. 107
AlgimantasBikelis
AnExtensionoftheConceptofSlowlyVaryingFunctionwith
ApplicationstoLargeDeviationLimitTheorems.......................... 127
AlexanderA.BorovkovandKonstantinA.Borovkov
Optimal and Asymptotically Optimal Controlfor Some
InventoryModels............................................................... 141
EkaterinaBulinskaya
vii
viii Contents
LevyPreservationandAssociatedPropertiesforf-Divergence
MinimalEquivalentMartingaleMeasures.................................. 163
SuzanneCawstonandLioudmilaVostrikova
Non-standardLimitTheoremsinNumberTheory ........................ 197
FrancescoCellarosiandYakovG.Sinai
AdditiveFunctionsandGaussianMeasures ................................ 215
LinanChenandDanielW.Stroock
FreeInfinitelyDivisibleApproximationsofn-Fold
FreeConvolutions.............................................................. 225
GennadiiChistyakovandFriedrichGo¨tze
AccurateApproximationofCorrelationCoefficientsbyShort
Edgeworth-ChebyshevExpansionandItsStatisticalApplications....... 239
GerdChristoph,VladimirV.Ulyanov,andYasunoriFujikoshi
TheStein-TikhomirovMethodandBerry-EsseenInequality
forSamplingSumsfromaFinitePopulationofIndependent
RandomVariables.............................................................. 261
ShakirK.FormanovandTamaraA.Formanova
OnOneInequalityforCharacteristicFunctions ........................... 275
NickoGamkrelidze
OntheNonlinearFilteringEquationsforSuperprocessesin
RandomEnvironment......................................................... 281
BroniusGrigelionis
UpperBoundsforBernsteinBasisFunctions............................... 293
VijayGuptaandTengizShervashidze
OnDistributionofZerosofRandomPolynomialsinComplexPlane.... 303
IldarIbragimovandDmitryZaporozhets
DependenceandInteractioninBranchingProcesses...................... 325
PeterJagersandFimaC.Klebaner
TestingFunctionalConnectionbetweenTwoRandomVariables......... 335
GyulaO.H.Katona
TheSymmetryGroupofGaussianStatesinL2.Rn/....................... 349
KalyanapuramR.Parthasarathy
Solution of the Optimal Stopping Problem for One-
DimensionalDiffusionBasedonaModificationofthePayoff
Function......................................................................... 371
ErnstPresman
Contents ix
PartII Interviews
TheTimesofYuriVasilyevichProkhorov................................... 407
FriedrichGo¨tzeandWillemR.vanZwet
AConversationwithYuriVasilyevichProkhorov.......................... 433
LarryShepp