| Theory of Stochastic Processes: With Applications to Financial Mathematics and Risk Theory 2010 Edition Contributor(s): Gusak, Dmytro (Author), Kukush, Alexander (Author), Kulik, Alexey (Author) |
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ISBN: 1461425069 ISBN-13: 9781461425069 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: May 2012 |
| Additional Information |
| BISAC Categories: - Mathematics | Probability & Statistics - General - Business & Economics | Statistics - Business & Economics | Finance - General |
| Dewey: 332.015 |
| Series: Problem Books in Mathematics |
| Physical Information: 0.8" H x 6.14" W x 9.21" (1.19 lbs) 376 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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- oreticalgrou |