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A weak convergence approach to the theory of large deviations [[electronic resource] /] / Paul Dupuis, Richard S. Ellis
| A weak convergence approach to the theory of large deviations [[electronic resource] /] / Paul Dupuis, Richard S. Ellis |
| Autore | Dupuis Paul |
| Pubbl/distr/stampa | New York, : Wiley, c1997 |
| Descrizione fisica | 1 online resource (506 p.) |
| Disciplina | 519.534 |
| Altri autori (Persone) | EllisRichard S <1947-> (Richard Steven) |
| Collana | Wiley series in probability and statistics. Probability and statistics |
| Soggetto topico |
Convergence
Large deviations |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-27400-0
9786613274007 1-118-16590-X 1-118-16589-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
A 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
3. 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. Cramér'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 4.5. 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 6 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 7.1. 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 8.5. Properties of the Rate Function |
| Record Nr. | UNINA-9910139594403321 |
Dupuis Paul
|
||
| New York, : Wiley, c1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
A weak convergence approach to the theory of large deviations [[electronic resource] /] / Paul Dupuis, Richard S. Ellis
| A weak convergence approach to the theory of large deviations [[electronic resource] /] / Paul Dupuis, Richard S. Ellis |
| Autore | Dupuis Paul |
| Pubbl/distr/stampa | New York, : Wiley, c1997 |
| Descrizione fisica | 1 online resource (506 p.) |
| Disciplina | 519.534 |
| Altri autori (Persone) | EllisRichard S <1947-> (Richard Steven) |
| Collana | Wiley series in probability and statistics. Probability and statistics |
| Soggetto topico |
Convergence
Large deviations |
| ISBN |
1-283-27400-0
9786613274007 1-118-16590-X 1-118-16589-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
A 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
3. 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. Cramér'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 4.5. 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 6 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 7.1. 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 8.5. Properties of the Rate Function |
| Record Nr. | UNINA-9910830133003321 |
|
Dupuis Paul
|
||
| New York, : Wiley, c1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
A weak convergence approach to the theory of large deviations [[electronic resource] /] / Paul Dupuis, Richard S. Ellis
| A weak convergence approach to the theory of large deviations [[electronic resource] /] / Paul Dupuis, Richard S. Ellis |
| Autore | Dupuis Paul |
| Pubbl/distr/stampa | New York, : Wiley, c1997 |
| Descrizione fisica | 1 online resource (506 p.) |
| Disciplina | 519.534 |
| Altri autori (Persone) | EllisRichard S <1947-> (Richard Steven) |
| Collana | Wiley series in probability and statistics. Probability and statistics |
| Soggetto topico |
Convergence
Large deviations |
| ISBN |
1-283-27400-0
9786613274007 1-118-16590-X 1-118-16589-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
A 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
3. 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. Cramér'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 4.5. 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 6 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 7.1. 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 8.5. Properties of the Rate Function |
| Record Nr. | UNINA-9910841896703321 |
|
Dupuis Paul
|
||
| New York, : Wiley, c1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||