Haullasi löytyi yhteensä 20 tuotettaHaluatko tarkentaa hakukriteerejä? Suosituimmat ensin Aakkosjärjestys Vuosijärjestys Viimeksi lisätyt Viimeksi julkaistut
Dmytro Gusak; Alexander Kukush; Alexey Kulik; Yuliya Mishura; Andrey Pilipenko Springer-Verlag New York Inc. (2009) Kovakantinen kirja
49,60 €
Dmytro Gusak; Alexander Kukush; Alexey Kulik; Yuliya Mishura; Andrey Pilipenko Springer (2012) Pehmeäkantinen kirja
49,60 €
Alexander Bach; Miossy Kulik Literatur-Quickie (2013) Lehtivihko, moniste
24,20 €
Alexander Bach; Missy Kulik Literatur-Quickie (2013) Lehtivihko, moniste
25,90 €
Alexander Kulik Society of Biblical Literature (2004) Pehmeäkantinen kirja
30,70 €
Alexander Kulik Brill Academic Publishers (2005) Kovakantinen kirja
187,20 €
Alexander Kulikov; Nikolay Vereshchagin Springer-Verlag Berlin and Heidelberg GmbH & Co. KG (2011) Pehmeäkantinen kirja
49,60 €
Alexander Kulik De Gruyter (2010) Kovakantinen kirja
347,90 €
Alexander S. Kulikov; Sergei O. Kuznetsov; Pavel Pevzner Springer International Publishing AG (2014) Pehmeäkantinen kirja
49,60 €
Alexander Kulik; Sergey Minov Oxford University Press (2016) Kovakantinen kirja
191,00 €
Alexander Kulik; Catherine Mary MacRobert; Svetlina Nikolova; Moshe Taube; Cynthia M. Vakareliyska Brill (2016) Kovakantinen kirja
267,80 €
Alexander S. Kulikov; Gerhard J. Woeginger Springer International Publishing AG (2016) Pehmeäkantinen kirja
49,60 €
Boris Kulik; Alexander Fridman IGI Global (2017) Kovakantinen kirja
254,20 €
Alexander Kulik; Gabriele Boccaccini; Lorenzo DiTommaso; David Hamidovic; Michael E. Stone Oxford University Press Inc (2019) Kovakantinen kirja
125,60 €
Alexander Kulik Harvard University Press (2024) Kovakantinen kirja
80,20 €
Alexander S. Kulikov (ed.); Sofya Raskhodnikova (ed.) Springer (2022) Pehmeäkantinen kirja
73,70 €
Alexander B. Rabinovich; Fred E. Stephenson; Olga I. Yakovenko; Evgueni A. Kulikov; Richard Thomson Springer (2031) Kovakantinen kirja
97,80 €
Margarita Eglit; Dewey H Hodges; Alexander N Golubiatnikov; Jacov Kamenjarzh; Vladimir P Karlikov; Andrei G Kulikovskii World Scientific Publishing Co Pte Ltd (1996) Kovakantinen kirja
134,60 €
Andre Bandrauk; M. V. Fedorov; Elisabeth Giacobino; Sergei Kilin; Sergei Kulik; Wolfgang Sandner; Alexander M. Sergeev SPIE Press (2007) Pehmeäkantinen kirja
223,50 €
Andrew V. Goldberg; Alexander S. Kulikov Springer International Publishing AG (2016) Pehmeäkantinen kirja
49,60 €
Theory of Stochastic Processes - With Applications to Financial Mathematics and Risk Theory
Thiscollectionofproblemsisplannedasatextbookforuniversitycoursesinthe theoryofstochasticprocessesandrelatedspecialcourses. Theproblemsinthebook haveawidespectrumofthelevelofdif cultyandcanbeusefulforreaderswith variouslevelsofmasteringinthetheoryofstochasticprocesses. Togetherwithte- nicalandillustrativeproblemsintendedforbeginners,thebookcontainsanumber ofproblemsoftheoreticalnaturethatcanbeusefulforstudentsandundergraduate studentsthatpursueadvancedstudiesinthetheoryofstochasticprocessesandits- plications. Amongothers,theimportantaimofthebookistoprovideateachingstaff anef cienttoolforpreparingseminarstudies,tests,andexamsconcerninguniversity coursesinthetheoryofstochasticprocessesandrelatedtopics. Whilecomposingthe book,theauthorshavepartiallyusedthecollectionsofproblemsinprobabilityt- ory[16,65,75,83]. Also,someexercisesandproblemsfromthemonographsand textbooks[4,9,19,22,82]wereused. Atthesametime,alargepartofourproblem bookcontainsoriginalmaterial. Thebookisorganizedasfollows. Theproblemsarecollectedintochapters,each chapterbeingdevotedtoacertaintopic. Atthebeginningofeachchapter,theth- reticalgroundsforthecorrespondingtopicaregivenbrie ytogetherwiththelistof bibliography,whichthereadercanuseinordertostudythistopicinmoredetail. For themostoftheproblems,eitherhintsorcompletesolutions(oranswers)aregiven, andsomeoftheproblemsareprovidedwithbothhintsandsolutions(answers). H- ever,theauthorsdonotrecommendthatareaderusethehintssystematically,because solvingaproblemwithoutassistanceismuchmoreusefulthanusingaready-made idea. Somestatementsthathaveaparticulartheoreticalinterestareformulatedon theoreticalgrounds,andtheirproofsareformulatedasproblemsforthereader. Such problemsaresuppliedwitheithercompletesolutionsordetailedhints. Inordertoworkwiththeproblembookef ciently,areadershouldbeacquainted withprobabilitytheory,calculus,andmeasuretheorywithinthescopeofresp- tiveuniversity courses. Standard notions, suchas random variable, measurability, independence, Lebesgue measure and integral, and so on are used without ad- tionaldiscussion. Allthenewnotionsandstatementsrequiredforsolvingthepr- lemsaregiveneitherontheoreticalgroundsorintheformulationsoftheproblems vii viii Preface straightforwardly. However,sometimesanotionisusedinthetextbeforeitsformal de nition. Forinstance,theWienerandPoissonprocessesareprocesseswithin- pendentincrementsandthusareformallyintroducedinaTheoreticalgroundsfor Chapter5,buttheseprocessesareusedwidelyintheproblemsofChapters2to4. Theauthorsrecommendthatareaderwhocomestoanunknownnotionorobject usetheIndexinorderto ndthecorrespondingformalde nition. Thesamerec- mendationconcernssomestandardabbreviationsandsymbolslistedattheendofthe book. Someproblemsinthebookformcycles:solutionstooneofthemaregrounded onstatementsofothersoronauxiliaryconstructionsdescribedinsomepreceding solutions. Sometimes,onthecontrary,itisproposedtoprovethesamestatement withindifferentproblemsusingessentiallydifferenttechniques. Theauthorsrec- mendareaderpayspeci cattentiontothesefruitfulinternallinksbetweenvarious topicsofthetheoryofstochasticprocesses. Everypartofthebookwascomposedsubstantiallybyoneauthor. Chapters1-6, and16arecomposedbyA. Kulik,Chapters7,12-15,18,and19byYu. Mishura, Chapters 8-10 by A. Pilipenko, Chapter 17 by A. Kukush, and Chapter 20 by D. Gusak. Chapter11waspreparedjointlybyD. GusakandA. Pilipenko. Atthe sametime,everyauthorhasmadeacontributiontootherpartsofthebookbyprop- ingseparateproblemsorcyclesofproblems,improvingpreliminaryversionsoft- oreticalgrounds,andeditingthe naltext. The authors would like to express their deep gratitude to M. Portenko and A. Ivanovfortheircarefulreadingofapreliminaryversionofthebookandva- ablecommentsthatledtosigni cantimprovementofthetext. Theauthorsarealso gratefultoT. Yakovenko,G. Shevchenko,O. Soloveyko, Yu. Kartashov, Yu. K- menko,A. Malenko,andN. Ryabovafortheirassistanceintranslation,preparing lesandpictures,andcomposingthesubjectindexandreferences. Thetheoryofstochasticprocessesisanextendeddiscipline,andtheauthors- derstandthattheproblembookinitscurrentformmaycausecriticalremarksfrom readers,concerningeitherthestructureofthebookorthecontentofseparatech- ters. Whilepublishingtheproblembookinitscurrentform,theauthorsareopenfor remarks,comments,andpropositions,andexpressinadvancetheirgratitudetoall theircorrespondents. Kyiv DmytroGusak December2008 AlexanderKukush AlexeyKulik YuliyaMishura AndreyPilipenko Contents 1 De?nition of stochastic process. Cylinder?-algebra, ?nite-dimensional distributions, the Kolmogorov theorem...1 Theoreticalgrounds ...1 Bibliography...3 Problems...3 Hints...7 AnswersandSolutions...9 2 Characteristics of a stochastic process. Mean and covariance functions. Characteristic functions...11 Theoreticalgrounds ...11 Bibliography...13 Problems...13 Hints...16 AnswersandSolutions...17 3 Trajectories. Modi?cations. Filtrations...21 Theoreticalgrounds ...21 Bibliography...24 Problems...24 Hints...29 AnswersandSolutions...31 4 Continuity. Differentiability. Integrability...33 Theoreticalgrounds ...33 Bibliography...34 Problems...34 Hints...38 AnswersandSolutions...40 ix x Contents 5 Stochastic processes with independent increments. Wiener and Poisson processes. Poisson point measures...
Tilaustuote | Arvioimme, että tuote lähetetään meiltä noin 4-5 viikossa |
Tilaa jouluksi viimeistään 27.11.2024