LEADER 05507nam 2200721 a 450 001 9911020439303321 005 20200520144314.0 010 $a9786613227997 010 $a9781283227995 010 $a1283227991 010 $a9781118164396 010 $a1118164393 010 $a9781118164402 010 $a1118164407 035 $a(CKB)2550000000043362 035 $a(EBL)818908 035 $a(OCoLC)757394280 035 $a(SSID)ssj0000544874 035 $a(PQKBManifestationID)11327816 035 $a(PQKBTitleCode)TC0000544874 035 $a(PQKBWorkID)10553718 035 $a(PQKB)11325313 035 $a(MiAaPQ)EBC818908 035 $a(PPN)250199033 035 $a(Perlego)2775053 035 $a(EXLCZ)992550000000043362 100 $a19941006d1996 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSequential stochastic optimization /$fR. Cairoli, Robert C. Dalang 210 $aNew York $cJ. Wiley & Sons$dc1996 215 $a1 online resource (348 p.) 225 1 $aWiley series in probability and mathematical statistics 300 $a"A Wiley-Interscience publication." 311 08$a9780471577546 311 08$a0471577545 320 $aIncludes bibliographical references and indexes. 327 $aSequential Stochastic Optimization; Contents; Preface; Notation and Conventions; 1. Preliminaries; 1.1 Filtered Probability Spaces; 1.2 Random Variables; 1.3 Stopping Points; 1.4 Increasing Paths and Accessible Stopping Points; 1.5 Some Operations on Accessible Stopping Points; 1.6 Stochastic Processes and Martingales; Exercises; Historical Notes; 2. Sums of Independent Random Variables; 2.1 Maximal Inequalities; 2.2 Integrability Criteria for the Supremum; 2.3 The Strong Law of Large Numbers; 2.4 Case Where the Random Variables Are Identically Distributed; Exercises; Historical Notes 327 $a3. Optimal Stopping3.1 Stating the Problem; 3.2 Snell's Envelope; 3.3 Solving the Problem; 3.4 A Related Problem; 3.5 Maximal Accessible Stopping Points; 3.6 Case Where the Index Set is Finite; 3.7 An Application to Normalized Partial Sums; 3.8 Complements; Exercises; Historical Notes; 4. Reduction to a Single Dimension; 4.1 Linear Representation of Accessible Stopping Points; 4.2 Applications; 4.3 Linear Representation in the Setting of Inaccessible Stopping Points; Exercises; Historical Notes; 5. Accessibility and Filtration Structure; 5.1 Conditions for Accessibility 327 $a5.2 Consequences for the Structure of the Filtration5.3 The Bidimensional Case; 5.4 Predictability of Optional Increasing Paths; 5.5 The Combinatorial Structure of a Filtration; 5.6 The Combinatorial Structure of a Filtration Satisfying COl; 5.7 Optimal Stopping and Linear Optimization; Exercises; Historical Notes; 6. Sequential Sampling; 6.1 Stating the Problem; 6.2 Constructing the Model; 6.3 The Reward Process and Snell's Envelope; 6.4 Describing the Optimal Strategy; 6.5 The Likelihood-Ratio Test; 6.6 Applications; 6.7 Complement; Exercises; Historical Notes; 7. Optimal Sequential Control 327 $a7.1 An Example7.2 Preliminaries; 7.3 Controls; 7.4 Optimization; 7.5 Optimization Over Finite Controls; 7.6 Case Where the Index Set Is Finite; 7.7 Extension to General Index Sets; Exercises; Historical Notes; 8. Multiarmed Bandits; 8.1 Formulating the Problem; 8.2 Index Controls; 8.3 Gittins Indices; 8.4 Characterizing Optimal Controls; 8.5 Examples; Exercises; Historical Notes; 9. The Markovian Case; 9.1 Markov Chains and Superharmonic Functions; 9.2 Optimal Control of a Markov Chain; 9.3 The Special Case of a Random Walk 327 $a9.4 Control and Stopping at the Time of First Visit to a Set of States9.5 Markov Structures; Exercises; Historical Notes; 10. Optimal Switching Between Two Random Walks; 10.1 Formulating and Solving the Problem; 10.2 Some Properties of the Solution; 10.3 The Structure of the Solution; 10.4 Constructing the Switching Curves; 10.5 Characterizing the Type of the Solution; 10.6 Determining the Type of the Solution; Exercises; Historical Notes; Bibliography; Index of Notation; Index of Terms 330 $aSequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved. Offering much material that is either new or has never before appeared in book form, it lucidly presents a unified theory of optimal stopping and optimal sequential control of stochastic processes. This book has been carefully organized so that little prior knowledge of the subject is assumed; its only prerequisites are a standard graduate course in probability theory and some familiarity with discrete-paramet 410 0$aWiley series in probability and mathematical statistics.$pApplied probability and statistics. 606 $aOptimal stopping (Mathematical statistics) 606 $aDynamic programming 606 $aStochastic control theory 615 0$aOptimal stopping (Mathematical statistics) 615 0$aDynamic programming. 615 0$aStochastic control theory. 676 $a519.2 700 $aCairoli$b R$g(Renzo),$f1931-1994.$01837694 701 $aDalang$b Robert C.$f1961-$0602758 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911020439303321 996 $aSequential stochastic optimization$94416486 997 $aUNINA