Labelled Markov processes:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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London
Imperial College Press
© 2009
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| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (pages 189-196) and index 1. Introduction. 1.1. Preliminary remarks. 1.2. Elementary discrete probability theory. 1.3. The need for measure theory. 1.4. The laws of large numbers. 1.5. Borel-Cantelli lemmas -- 2. Measure theory. 2.1. Measurable spaces. 2.2. Measurable functions. 2.3. Metric spaces and properties of measurable functions. 2.4. Measurable spaces of sequences. 2.5. Measures. 2.6. Lebesgue measure. 2.7. Nonmeasurable sets. 2.8. Exercises -- 3. Integration. 3.1. The definition of integration. 3.2. Properties of the integral. 3.3. Riemann integrals. 3.4. Multiple integrals. 3.5. Exercises -- 4. The Radon-Nikodym theorem. 4.1. Set functions. 4.2. Decomposition theorems. 4.3. Absolute continuity. 4.4. Exercises -- 5. A category of stochastic relations. 5.1. The category of SRel. 5.2. Probability monads. 5.3. The structure of SRel. 5.4. Kozen semantics and duality. 5.5. Exercises -- - 6. Probability theory on continuous spaces. 6.1. Probability spaces. 6.2. Random variables. 6.3. Conditional probability. 6.4. Regular conditional probability. 6.5. Stochastic processes and Markov processes -- 7. Bisimulation for labelled Markov processes. 7.1. Ordinary bisimulation. 7.2. Probabilistic bisimulation for discrete systems. 7.3. Two examples of continuous-state processes. 7.4. The definition of labelled Markov processes. 7.5. Basic facts about analytic spaces. 7.6. Bisimulation for labelled Markov processes. 7.7. A logical characterisation of bisimulation -- 8. Metrics for labelled Markov processes. 8.1. From bisimulation to a metric. 8.2. A real-valued logic on labelled Markov processes. 8.3. Metrics on processes. 8.4. Metric reasoning for process algebras. 8.5. Perturbation. 8.6. The asymptotic metric. 8.7. Behavioural properties of the metric. 8.8. The pseudometric as a maximum fixed point -- - 9. Approximating labelled Markov processes. 9.1. An explicit approximation construction. 9.2. Dealing with loops. 9.3. Adapting the approximation to formulas -- 10. Approximating the approximation -- 11. A domain of labelled Markov processes. 11.1. Background on domain theory. 11.2. The domain Proc. 11.3. L[symbol] as the logic of Proc. 11.4. Relating Proc and LMP -- 12. Real-time and continuous stochastic logic. 12.1. Background. 12.2. Spaces of paths in a CTMP. 12.3. The Logic CSL. 12.4. A general technique for relating bisimulation and logic. 12.5. Bisimilarity and CSL -- 13. Related work. 13.1. Mathematical foundations. 13.2. Metrics. 13.3. Nondeterminism. 13.4. Testing. 13.5. Weak bisimulation. 13.6. Approximation. 13.7. Model checking Labelled Markov processes are probabilistic versions of labelled transition systems with continuous state spaces. The book covers basic probability and measure theory on continuous state spaces and then develops the theory of LMPs. The main topics covered are bisimulation, the logical characterization of bisimulation, metrics and approximation theory. An unusual feature of the book is the connection made with categorical and domain theoretic concepts |
| Beschreibung: | 1 Online-Ressource (xii, 199 pages) |
| ISBN: | 1848162871 1848162898 9781848162877 9781848162891 |
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| 500 | |a Includes bibliographical references (pages 189-196) and index | ||
| 500 | |a 1. Introduction. 1.1. Preliminary remarks. 1.2. Elementary discrete probability theory. 1.3. The need for measure theory. 1.4. The laws of large numbers. 1.5. Borel-Cantelli lemmas -- 2. Measure theory. 2.1. Measurable spaces. 2.2. Measurable functions. 2.3. Metric spaces and properties of measurable functions. 2.4. Measurable spaces of sequences. 2.5. Measures. 2.6. Lebesgue measure. 2.7. Nonmeasurable sets. 2.8. Exercises -- 3. Integration. 3.1. The definition of integration. 3.2. Properties of the integral. 3.3. Riemann integrals. 3.4. Multiple integrals. 3.5. Exercises -- 4. The Radon-Nikodym theorem. 4.1. Set functions. 4.2. Decomposition theorems. 4.3. Absolute continuity. 4.4. Exercises -- 5. A category of stochastic relations. 5.1. The category of SRel. 5.2. Probability monads. 5.3. The structure of SRel. 5.4. Kozen semantics and duality. 5.5. Exercises -- | ||
| 500 | |a - 6. Probability theory on continuous spaces. 6.1. Probability spaces. 6.2. Random variables. 6.3. Conditional probability. 6.4. Regular conditional probability. 6.5. Stochastic processes and Markov processes -- 7. Bisimulation for labelled Markov processes. 7.1. Ordinary bisimulation. 7.2. Probabilistic bisimulation for discrete systems. 7.3. Two examples of continuous-state processes. 7.4. The definition of labelled Markov processes. 7.5. Basic facts about analytic spaces. 7.6. Bisimulation for labelled Markov processes. 7.7. A logical characterisation of bisimulation -- 8. Metrics for labelled Markov processes. 8.1. From bisimulation to a metric. 8.2. A real-valued logic on labelled Markov processes. 8.3. Metrics on processes. 8.4. Metric reasoning for process algebras. 8.5. Perturbation. 8.6. The asymptotic metric. 8.7. Behavioural properties of the metric. 8.8. The pseudometric as a maximum fixed point -- | ||
| 500 | |a - 9. Approximating labelled Markov processes. 9.1. An explicit approximation construction. 9.2. Dealing with loops. 9.3. Adapting the approximation to formulas -- 10. Approximating the approximation -- 11. A domain of labelled Markov processes. 11.1. Background on domain theory. 11.2. The domain Proc. 11.3. L[symbol] as the logic of Proc. 11.4. Relating Proc and LMP -- 12. Real-time and continuous stochastic logic. 12.1. Background. 12.2. Spaces of paths in a CTMP. 12.3. The Logic CSL. 12.4. A general technique for relating bisimulation and logic. 12.5. Bisimilarity and CSL -- 13. Related work. 13.1. Mathematical foundations. 13.2. Metrics. 13.3. Nondeterminism. 13.4. Testing. 13.5. Weak bisimulation. 13.6. Approximation. 13.7. Model checking | ||
| 500 | |a Labelled Markov processes are probabilistic versions of labelled transition systems with continuous state spaces. The book covers basic probability and measure theory on continuous state spaces and then develops the theory of LMPs. The main topics covered are bisimulation, the logical characterization of bisimulation, metrics and approximation theory. An unusual feature of the book is the connection made with categorical and domain theoretic concepts | ||
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| 650 | 4 | |a Markov processes | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Panangaden, Prakash 1954- |
| author_GND | (DE-588)139823573 |
| author_facet | Panangaden, Prakash 1954- |
| author_role | aut |
| author_sort | Panangaden, Prakash 1954- |
| author_variant | p p pp |
| building | Verbundindex |
| bvnumber | BV043067389 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)613682483 (DE-599)BVBBV043067389 |
| dewey-full | 519.233 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.233 |
| dewey-search | 519.233 |
| dewey-sort | 3519.233 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043067389 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:16:26Z |
| institution | BVB |
| isbn | 1848162871 1848162898 9781848162877 9781848162891 |
| language | English |
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| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xii, 199 pages) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
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| spelling | Panangaden, Prakash 1954- Verfasser (DE-588)139823573 aut Labelled Markov processes Prakash Panangaden London Imperial College Press © 2009 1 Online-Ressource (xii, 199 pages) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (pages 189-196) and index 1. Introduction. 1.1. Preliminary remarks. 1.2. Elementary discrete probability theory. 1.3. The need for measure theory. 1.4. The laws of large numbers. 1.5. Borel-Cantelli lemmas -- 2. Measure theory. 2.1. Measurable spaces. 2.2. Measurable functions. 2.3. Metric spaces and properties of measurable functions. 2.4. Measurable spaces of sequences. 2.5. Measures. 2.6. Lebesgue measure. 2.7. Nonmeasurable sets. 2.8. Exercises -- 3. Integration. 3.1. The definition of integration. 3.2. Properties of the integral. 3.3. Riemann integrals. 3.4. Multiple integrals. 3.5. Exercises -- 4. The Radon-Nikodym theorem. 4.1. Set functions. 4.2. Decomposition theorems. 4.3. Absolute continuity. 4.4. Exercises -- 5. A category of stochastic relations. 5.1. The category of SRel. 5.2. Probability monads. 5.3. The structure of SRel. 5.4. Kozen semantics and duality. 5.5. Exercises -- - 6. Probability theory on continuous spaces. 6.1. Probability spaces. 6.2. Random variables. 6.3. Conditional probability. 6.4. Regular conditional probability. 6.5. Stochastic processes and Markov processes -- 7. Bisimulation for labelled Markov processes. 7.1. Ordinary bisimulation. 7.2. Probabilistic bisimulation for discrete systems. 7.3. Two examples of continuous-state processes. 7.4. The definition of labelled Markov processes. 7.5. Basic facts about analytic spaces. 7.6. Bisimulation for labelled Markov processes. 7.7. A logical characterisation of bisimulation -- 8. Metrics for labelled Markov processes. 8.1. From bisimulation to a metric. 8.2. A real-valued logic on labelled Markov processes. 8.3. Metrics on processes. 8.4. Metric reasoning for process algebras. 8.5. Perturbation. 8.6. The asymptotic metric. 8.7. Behavioural properties of the metric. 8.8. The pseudometric as a maximum fixed point -- - 9. Approximating labelled Markov processes. 9.1. An explicit approximation construction. 9.2. Dealing with loops. 9.3. Adapting the approximation to formulas -- 10. Approximating the approximation -- 11. A domain of labelled Markov processes. 11.1. Background on domain theory. 11.2. The domain Proc. 11.3. L[symbol] as the logic of Proc. 11.4. Relating Proc and LMP -- 12. Real-time and continuous stochastic logic. 12.1. Background. 12.2. Spaces of paths in a CTMP. 12.3. The Logic CSL. 12.4. A general technique for relating bisimulation and logic. 12.5. Bisimilarity and CSL -- 13. Related work. 13.1. Mathematical foundations. 13.2. Metrics. 13.3. Nondeterminism. 13.4. Testing. 13.5. Weak bisimulation. 13.6. Approximation. 13.7. Model checking Labelled Markov processes are probabilistic versions of labelled transition systems with continuous state spaces. The book covers basic probability and measure theory on continuous state spaces and then develops the theory of LMPs. The main topics covered are bisimulation, the logical characterization of bisimulation, metrics and approximation theory. An unusual feature of the book is the connection made with categorical and domain theoretic concepts MATHEMATICS / Probability & Statistics / Stochastic Processes bisacsh Markov processes Measure theory World Scientific (Firm) Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=305142 Aggregator Volltext |
| spellingShingle | Panangaden, Prakash 1954- Labelled Markov processes MATHEMATICS / Probability & Statistics / Stochastic Processes bisacsh Markov processes Measure theory |
| title | Labelled Markov processes |
| title_auth | Labelled Markov processes |
| title_exact_search | Labelled Markov processes |
| title_full | Labelled Markov processes Prakash Panangaden |
| title_fullStr | Labelled Markov processes Prakash Panangaden |
| title_full_unstemmed | Labelled Markov processes Prakash Panangaden |
| title_short | Labelled Markov processes |
| title_sort | labelled markov processes |
| topic | MATHEMATICS / Probability & Statistics / Stochastic Processes bisacsh Markov processes Measure theory |
| topic_facet | MATHEMATICS / Probability & Statistics / Stochastic Processes Markov processes Measure theory |
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