LEADER 05446nam 2200649Ia 450 001 9910139594403321 005 20170809165506.0 010 $a1-283-27400-0 010 $a9786613274007 010 $a1-118-16590-X 010 $a1-118-16589-6 035 $a(CKB)2550000000054361 035 $a(EBL)818933 035 $a(OCoLC)757486970 035 $a(SSID)ssj0000550647 035 $a(PQKBManifestationID)11360299 035 $a(PQKBTitleCode)TC0000550647 035 $a(PQKBWorkID)10509205 035 $a(PQKB)11752480 035 $a(MiAaPQ)EBC818933 035 $a(EXLCZ)992550000000054361 100 $a19960724d1997 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 12$aA weak convergence approach to the theory of large deviations$b[electronic resource] /$fPaul Dupuis, Richard S. Ellis 210 $aNew York $cWiley$dc1997 215 $a1 online resource (506 p.) 225 1 $aWiley series in probability and statistics. Probability and statistics 300 $aDescription based upon print version of record. 311 $a0-471-07672-4 320 $aIncludes bibliographical references (p. 458-462) and indexes. 327 $aA Weak Convergence Approach to the Theory of Large Deviations; Preface; Contents; 1. Formulation of Large Deviation Theory in Terms of the Laplace Principle; 1.1. Introduction; 1.2. Equivalent Formulation of the Large Deviation Principle; 1.3. Basic Results in the Theory; 1.4. Properties of the Relative Entropy; 1.5. Stochastic Control Theory and Dynamic Programming; 2. First Example: Sanov's Theorem; 2.1. Introduction; 2.2. Statement of Sanov's Theorem; 2.3. The Representation Formula; 2.4. Proof of the Laplace Principle Lower Bound; 2.5. Proof of the Laplace Principle Upper Bound 327 $a3. Second Example: Mogulskii's Theorem3.1. Introduction; 3.2. The Representation Formula; 3.3. Proof of the Laplace Principle Upper Bound and Identification of the Rate Function; 3.4. Statement of Mogulskii's Theorem and Completion of the Proof; 3.5. Crame?r's Theorem; 3.6. Comments on the Proofs; 4 Representation Formulas for Other Stochastic Processes; 4.1. Introduction; 4.2. The Representation Formula for the Empirical Measures of a Markov Chain; 4.3. The Representation Formula for a Random Walk Model; 4.4. The Representation Formula for a Random Walk Model with State-Dependent Noise 327 $a4.5. Extensions to Unbounded Functions4.6. Representation Formulas for Continuous-Time Markov Processes; 4.6.1. Introduction; 4.6.2. Formal Derivation of Representation Formulas for Continuous-Time Markov Processes; 4.6.3. Examples of Continuous-Time Representation Formulas; 4.6.4. Remarks on the Proofs of the Representation Formulas; 5 Compactness and Limit Properties for the Random Walk Model; 5.1. Introduction; 5.2. Definitions and a Representation Formula; 5.3. Compactness and Limit Properties; 5.4. Weaker Version of Condition 5.3.1 327 $a6 Laplace Principle for the Random Walk Model with Continuous Statistics6.1. Introduction; 6.2. Proof of the Laplace Principle Upper Bound and Identification of the Rate Function; 6.3. Statement of the Laplace Principle; 6.4. Strategy for the Proof of the Laplace Principle Lower Bound; 6.5. Proof of the Laplace Principle Lower Bound Under Conditions 6.2.1 and 6.3.1; 6.6. Proof of the Laplace Principle Lower Bound Under Conditions 6.2.1 and 6.3.2; 6.7. Extension of Theorem 6.3.3 To Be Applied in Chapter 10; 7. Laplace Principle for the Random Walk Model with Discontinuous Statistics 327 $a7.1. Introduction7.2. Statement of the Laplace Principle; 7.3. Laplace Principle for the Final Position Vectors and One-Dimensional Examples; 7.4. Proof of the Laplace Principle Upper Bound; 7.5. Proof of the Laplace Principle Lower Bound; 7.6. Compactness of the Level Sets of Ix; 8. Laplace Principle for the Empirical Measures of a Markov Chain; 8.1. Introduction; 8.2. Compactness and Limit Properties of Controls and Controlled Processes; 8.3. Proof of the Laplace Principle Upper Bound and Identification of the Rate Function; 8.4. Statement of the Laplace Principle 327 $a8.5. Properties of the Rate Function 330 $aApplies the well-developed tools of the theory of weak convergence of probability measures to large deviation analysis--a consistent new approachThe theory of large deviations, one of the most dynamic topics in probability today, studies rare events in stochastic systems. The nonlinear nature of the theory contributes both to its richness and difficulty. This innovative text demonstrates how to employ the well-established linear techniques of weak convergence theory to prove large deviation results. Beginning with a step-by-step development of the approach, the book skillfully guides r 410 0$aWiley series in probability and statistics.$pProbability and statistics. 606 $aConvergence 606 $aLarge deviations 608 $aElectronic books. 615 0$aConvergence. 615 0$aLarge deviations. 676 $a519.534 700 $aDupuis$b Paul$059509 701 $aEllis$b Richard S$g(Richard Steven),$f1947-$0476698 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910139594403321 996 $aWeak convergence approach to the theory of large deviations$91572344 997 $aUNINA