Stochastic Processes, Statistical Methods, and Engineering Mathematics: SPAS 2019, Västerås, Sweden, September 30–October 2 PDF
Preview Stochastic Processes, Statistical Methods, and Engineering Mathematics: SPAS 2019, Västerås, Sweden, September 30–October 2
Springer Proceedings in Mathematics & Statistics Anatoliy Malyarenko Ying Ni Milica Rančić Sergei Silvestrov Editors Stochastic Processes, Statistical Methods, and Engineering Mathematics SPAS 2019, Västerås, Sweden, September 30–October 2 Springer Proceedings in Mathematics & Statistics Volume 408 This book series features volumes composed of selected contributions from workshops and conferences in all areas of current research in mathematics and statistics,includingdatascience,operationsresearchandoptimization.Inaddition to an overall evaluation of the interest, scientific quality, and timeliness of each proposalatthehandsofthepublisher,individualcontributionsareallrefereedtothe highqualitystandardsofleadingjournalsinthefield.Thus,thisseriesprovidesthe researchcommunitywithwell-edited,authoritativereportsondevelopmentsinthe mostexcitingareasofmathematicalandstatisticalresearchtoday. · · · Anatoliy Malyarenko Ying Ni Milica Rancˇic´ Sergei Silvestrov Editors Stochastic Processes, Statistical Methods, and Engineering Mathematics SPAS 2019, Västerås, Sweden, September 30–October 2 Editors AnatoliyMalyarenko YingNi DivisionofMathematicsandPhysics DivisionofMathematicsandPhysics MälardalenUniversity MälardalenUniversity Västerås,Sweden Västerås,Sweden MilicaRancˇic´ SergeiSilvestrov DivisionofMathematicsandPhysics DivisionofMathematicsandPhysics MälardalenUniversity MälardalenUniversity Västerås,Sweden Västerås,Sweden ISSN 2194-1009 ISSN 2194-1017 (electronic) SpringerProceedingsinMathematics&Statistics ISBN 978-3-031-17819-1 ISBN 978-3-031-17820-7 (eBook) https://doi.org/10.1007/978-3-031-17820-7 MathematicsSubjectClassification:62P05,60H10,60F17,60K15,62M10,65C30,65K10 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. 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ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface This volume originated on the basis of selected contributions presented at the international conference “Stochastic Processes and Algebraic Structures—From TheoryTowardsApplications”(SPAS2019).Agroupofmathematicians,researchers from related areas, and practitioners from industry, who contribute to the areas of StochasticProcesses,StatisticalMethods,EngineeringMathematics,andAlgebraic Structures,participatedintheconference,whichhasbeenorganizedbytheDivision ofMathematicsandPhysicsattheMälardalenUniversityinVästerås,Sweden,and hasbeenheldonSeptember30–October2,2019. ThescopeofthevolumeisStochasticProcesses,StatisticalMethods,andEngi- neeringMathematics.TheaccompanyingvolumecontainscontributionstoAlgebraic Structures. The purpose of the book is to highlight the latest advances in the above areas and focus on the mathematical structures, models, concepts, problems, computa- tionalmethods,andalgorithmsthatareimportantforapplicationsinvariousfields ofscienceandsociety. Thevolumeisdividedintothreeparts,accordingtotheareasofthebook’sscope describedabove. Part I, called “Stochastic Processes and Analysis”, contains 21 Chapters. Chapter 1, written by Mohammed Albuhayri, Christopher Engström, Anatoliy Malyarenko, Ying Ni, and Sergei Silvestrov, is concerned with the double-mean- revertingmodelproposedbyJimGatheral.Theasymptoticexpansionoftheimplied volatilityofaEuropeancalloptionwrittenonastockintheabovemodelisimproved uptoorder3. Chapter2,writtenbyMohammadJamsherAliandKalevPärna,studiestheruin probabilityofthesumoftwoclassicalriskprocessesundertheassumptionthatthe claimsizedistributionsareofphasetypeandthatthetwoPoissonprocessesofclaim arrivalsarecorrelated.Anexactformulafortheruinprobabilityofthemergedrisk processisconstructed. Chapter3byTinNweAyeandLinusCarlssonstudiesanaquaticecologicalsystem containingonefishspeciesandanunderlyingresource.Thismodelisinvestigatedin boththedeterministicandthestochasticsettings.Theauthorsprovideestimatesfor v vi Preface theexpectedoutcomeofpopulationproperties,measuresofdispersion,probability ofextinction,andtherecoverypotentialofaspecies,amongothers. Chapter4byDomingosDjinja,SergeiSilvestrov,andAlexBehakaniraTumwe- sigyeisdevotedtopairsofintegraloperatorsonthespacesL overarbitrarymeasure p spaces.Theauthorsobtainconditionsonthekernelsofintegraloperatorstosatisfy general covariance type commutation relations associated to polynomial actions important in applications of noncommutative analysis, noncommutative geometry, andoperatoralgebramethodsinstochasticprocesses,harmonicanalysis,quantum physics,andengineering. Chapter5byVitaliyGolomoziystudiesthefirstsimultaneoushittingoftheatom bytwodiscrete-time,inhomogeneousMarkovchainswithvaluesinageneralphase space.Bothconditionsfortheexistenceandcomputableboundsforthehittingtime’s exponentialmomentareestablished. Chapter6,writtenbyLuJin,MarkoDimitrov,andYingNi,considersthepricing ofAmericanoptionswhentheunderlyingassetisgovernedbytheMarkovregime- switchingprocess.Theexistenceofamonotonicoptimalexercisepolicywithrespect totheholdingtime,assetprice,andeconomicconditionsisproved. Chapter 7 by Ya. M. Khusanbaev and Kh. E. Kudratov gives the upper bounds formomentsandcentralmomentsofbranchingprocessesinavaryingenvironment startingwitharandomnumberofparticles. InChap.8,writtenbyAbderrahimKitouniandFatihaMessaci,afunctionallaw of the iterated logarithm for the increment functions of empirical processes with twicecensoreddataisestablished.Stronglawsforkernelestimatorsofthedensity andthefailurerateofthelifetimearealsoderived. Chapter 9 by Pavlos Kolias and Alexandra Papadopoulou describes a DNA sequence by a semi-Markov chain with discrete state space consisting of the four nucleotides. Both strong and weak d-periodic and quasiperiodic behaviour of this modelischaracterizedbyequationsinclosedanalyticform.Therelatedprobabilities andthecorrespondingindexesareprovided. In Chap. 10, Sergey Krasnitskiy, Oleksandr Kurchenko, and Olga Syniavska proveaBaxter-typetheoremforGaussiangeneralizedrandomprocesseswithinde- pendent values. Sufficient conditions for the singularity of probability measures correspondingtosuchprocessesarealsogiven. InChap.11,EugeneLebedev,VadymPonomarov,andHannaLivinskainvestigate abivariateMarkovprocess.Thestatespaceoftheprocessisalatticesemi-strip.Such amodeldescribestheservicepolicyofamulti-serverretrialqueueinwhichtherate of repeated flow does not depend on the number of sources of repeated calls. The ergodicityconditionsandavector-matrixrepresentationofsteadystatedistribution areobtained. InChap.12,AnatoliyMalyarenkoandHosseinNohrouzianusecubatureformulae ofdegrees5and7onWienerspacetopriceEuropeanoptionsintheclassicalBlack- Scholesmodel.Theobtainednumericalresultsarecomparedwiththewell-known Nobelprize-awarded closedformsolution,andseveral importantproperties ofthe cubaturemethodsareestablished. Preface vii In Chap. 13, Yuliya Mishura, Georgiy Shevchenko, and Sergiy Shklyar study Volterra processes. The celebrated fractional Brownian motion appears here as a particularcase.Thesmoothnesspropertiesoftheaboveprocesses,includingconti- nuityandHölderproperty,areestablished.Theproblemofinverserepresentationof thestandardBrownianmotionviaaVolterraprocessisinvestigated. InChap.14,GiuliaDiNunno,YuliyaMishura,andKostiantynRalchenkostudy the existence and uniqueness of solutions to stochastic differential equations with VolterraprocessesdrivenbyLévynoise.Specialattentionisgiventotwokindsof Volterra-Gaussian processes that generalize the compact interval representation of fractionalBrownianmotiontostochasticequationswithsuchprocesses. InChaps.15–17,TalatNazirandSergeiSilvestrovinvestigatetheexistenceand otherpropertiesoffixedpoints,jointfixedpoints,andperiodicpointsformappings andpairsofmappingsonmultiplicativemetricspacessatisfyingvariousgeneralized contractionandcyclicconditions. InChap.18,GodwinAmechiOkeke,MujahidAbbas,andSergeiSilvestrovintro- ducearandomversionofsomeknownfastfixedpointiterativeprocesses,approxi- matetherandomfixedpointofageneralizedrandomoperatorusingtheserandom iterativeprocesses,andprovetheBochnerintegrabilityoftherandomfixedpoints forthiskindofgeneralizedrandomoperatorsandthealmostsureT-stabilityofthe aboverandomiterativeprocesses. In Chap. 19, Salvador Cruz Rambaud presents mathematical results for the absence of asset price bubbles by using, as an algebraic tool, a state-price deflator across an infinite time horizon. A financial market with both uncertainty, a finite number of corporate securities, and a countable number of trading dates is investigatedthere. José L. da Silva, Custódia Drumond, and Ludwig Streit give an account of the formfactorsofpathsforacertainclassofnon-GaussianprocessesinChap.20.A closedanalyticformfortheformfactorsandtheDebyefunctionareobtained.The relation between the mean square end-to-end length and the radius of gyration is explicitlyderived. In Chap. 21, Dmitrii Silvestrov obtains necessary and sufficient conditions for convergence in distribution and in Skorokhod J-topology for counting processes generatedbyflowsofrareeventsforperturbedsemi-Markovprocesses. PartII,called“StatisticalMethods”,contains7chapters.Itbeginswiththechapter by Guglielmo D’Amico, Bice Di Basilio, Filippo Petroni, and Fulvio Gismondi (Chap.22),inwhichtwodrawdown-basedriskmeasuresformanagingmarketcrisis areconsidered.Thesetwomeasuresarethenanalysedusinghigh-frequencymarket dataandsyntheticdatageneratedbyARMA,GARCH,andEGARCHmodels. Chapter23byVladimirAnisimovandMatthewAustindealswithpatientenrol- ment modelling and forecasting. Here, modelling of enrolment on different levels and with restrictions are discussed, and new analytical techniques are proposed to findthesolutiontothecorrespondingoptimizationproblem. Chapter 24 by Collins Anguzu, Christopher Engström, Henry Kasumba, John MageroMango,andSergeiSilvestrovdealswithcentralitymeasuresingraphtheory. viii Preface Algorithms are developed for recalculating two centrality measures, namely alpha andeigenvectorcentralitymeasures,usinggraphpartitioningtechniques. In Chap. 25 by Yuriy Kozachenko and Iryna Rozora, estimation of the impulse response function of a time-invariant continuous linear system with a real-valued impulse response function was considered. Statistical properties of this impulse responsefunctionandcriteriononitsshapearegiven. Chapters26and27,byAsaphKeikaraMuhumuza,KarlLundengård, Anatoliy Malyarenko, Sergei Silvestrov, John Magero Mango, and Godwin Kakuba, are devotedtousefulapplicationsofextremepointsforVandermondedeterminants.In Chap.26,theextremepoints,optimizedonvarioussurfaces,areusedtoconductthe risk-minimizationtaskinassetpricingandoptimalportfolioselection.InChap.27, the extreme points maximize the Wishart probability distribution based on the boundaryofthesymmetricconesinJordanalgebra. Finally,Part2endswithChap.28byNataliyaShchestyukandSerhiiTyshchenko proposing a new approach to option pricing. A concept of investor optimal price is defined as the optimal decision of a investor maximizing expected profit. This investor optimal pricing, integrated with risk management, is then conducted by stochasticoptimization. Part III, called “Engineering Mathematics”, contains 12 chapters. Chapter 29 by Magnus Ögren deals with the one-dimensional Stefan problem with a general time-dependentboundaryconditionatthefixedboundary.Applyingdiscreterandom walks,stochasticsolutionshavebeenobtainedandconfirmedagainstanalyticalor numericalsolutions(FDM). InChap.30,DoghonayArjmandexploresthepossibilityofintegratingperfectly matched layers to the local wave equation. In particular, questions in relation to accuracyandreducedcomputationalcostsareaddressed.Numericalsimulationsare providedinasimplifiedone-dimensionalsettingtoillustratetheideas. The objective of the work done by Imran M. Chandarki and Brijbhan Singh in Chap.31wastorevisittheproblempertainingtoaverticallyflowingfluidpasseda modelofathinverticalfininasaturatedporousmedium.Thegoverningequations havebeensimplifiedusingthesimilaritytransformationtoyieldordinarydifferential equations.Theseequationshavebeensolvedbyhomotopyanalysismethod(HAM). InChap.32,Vucˇkovic´ etal.presentmodellingofapermanentmagnetshapedas truncated cone and positioned in the vicinity of a body of finite dimensions made of soft magnetic material. The force calculation between the permanent magnet andsoftmagneticcylinderisperformedusingthehybridboundaryelementmethod alongwithsemi-analyticalapproachbasedonfictitiousmagnetizationchargesand discretizationtechnique. Chapters33and32tackleproblemsrelatedtothepopulationdynamics.Specif- ically, in Chap. 33, Loy Nankinga and Linus Carlsson deal with interactions of a consumer-resource system with harvesting in which African Catfish consumes the foodresource.ThedynamicsofthefoodresourceandtheAfricanCatfishresultin asystemofordinarydifferentialequationscalledastage-structuredfishpopulation model.Analysisofeightharvestingscenariosrevealedthatharvestinglargejuveniles Preface ix andsmalladultsunderequalharvestingratesgivesthehighestmaximumsustainable yieldcomparedtootherharvestingscenarios. In Chap. 34, Sam Canpwonyi and Linus Carlsson studied dynamics of forage resourceandlivestockpopulationinagrasslandecosystemdescribingitbycoupled ordinary differential equations. By solving this system, one is able to predict the density-dependentpropertiesofthepopulationsincethesystemprovidesasomewhat close-to-realitydescriptionofthenaturalandtraditionalgrazingsystem. In Chaps. 35–38 by Prashant G. Metri and coauthors, numerical and analytical methodsareappliedtoinvestigationofsolutionsofboundaryandinitialvalueprob- lemsforsystemsofpartialdifferentialequationinfluidmechanicsandelectromag- netism applications, including magnetohydrodynamic Casson nanofluid flow over anonlinearstretchingsheetwithvelocityslipandconvectiveboundaryconditions, mathematicalandcomputational analysisofMHDviscoelasticfluidflowandheat transferoverstretchingsurfaceembeddedinasaturatedporousmedium,numerical solutionofboundarylayerflowproblemofaMaxwellfluidpastaporousstretching surface,andeffectofelectromagneticfieldonmixedconvectionoftwoimmiscible conductingfluidsinaverticalchannel. Finally, Chaps. 39 and 40 cover new stochastic digital measurement method (SDMM)anditsroleindesigninglow-costdigitalhighprecisionpowergridelec- tricalenergymeters.InChap.39,authoredbyVujicˇic´etal,mathematicalproperties oftheSDMMaregiven.Practicalandusefulformulasarederivedthatconnectthe measurementparameterswiththeprecision.Hardwareofatwo-bitSDMMissimple, sosourcesofsystematicerrorscaneasilybeidentifiedanderrorcorrected.Inaddition, simplehardwareenableslarge-scaleparallelizationofmeasurementsandprocessing. UsingthemultibitSMI(StochasticMeasurementInstruments)mathematicalmodel developedin39and40,aworkinghardwareprototypeofa4-bitSDEEM(Stochastic DigitalElectricalEnergyMeter)wasbuiltandrigorouslytestedbyMarjanUrekar andJelenaDjordjevic´Kozarov.Thisconfirmedthevalidityofthetheoreticalmodel andthatSDEEMisanidealsolutionforaSmartMeterinSmartGridinIndustry4.0 applications,duetoitshighprecisionandaccuracy,highreliability,digitalcontrols andeaseofinterfacingwithIoTandIIoT,simplehardware,andlowcost. The volume is intended for researchers, graduate and Ph.D. students, and prac- titionersintheareasofMathematics,Statistics,Finance,andEngineering,whoare interestedinasourceforinspiration,cutting-edgeresearch,andapplications. Thisbookcomprisesselectedrefereedcontributionsfromseverallargeresearch communities in modern stochastic processes, probability theory, statistics, anal- ysis,computationalmathematics,engineeringmathematics,andtheirinterplayand applications. The book will be a useful source of inspiration for a broad spec- trumofresearchersandresearchstudentsinthefieldofMathematicsandApplied Mathematics,aswellasinthespecificareasofapplicationsconsideredinthebook. This collective book project has been realized thanks to the strategic support offeredbyMälardalenUniversityfortheresearchandresearcheducationinMath- ematicswhichisconductedbytheresearchenvironmentMathematicsandApplied Mathematics (MAM) in the established research specialization of Educational SciencesandMathematicsattheSchoolofEducation,CultureandCommunicationat
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