| 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: 0387878610 ISBN-13: 9780387878614 Publisher: Springer OUR PRICE: $52.24 Product Type: Hardcover - Other Formats Published: December 2009 Annotation: The book is a collection of problems in the theory of stochastic processes and its application to financial mathematics and risk theory. More than 1000 problems are divided into 23 chapters. Each chapter is supplied by the brief overview of the main theoretical results. Most of the problems are supplied by either solutions or hints to the solutions. |
| Additional Information |
| BISAC Categories: - Mathematics | Probability & Statistics - General - Business & Economics | Statistics |
| Dewey: 332.015 |
| LCCN: 2009939131 |
| Series: Problem Books in Mathematics |
| Physical Information: 1" H x 6.14" W x 9.21" (1.70 lbs) 388 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 |