# Labelled Markov processes /

**Saved in:**

Author / Creator: | Panangaden, P. (Prakash) |
---|---|

Imprint: | London : Imperial College Press ; Singapore : Distributed by World Scientific Pub. Co., ©2009. |

Description: | 1 online resource (xii, 199 pages) : illustrations |

Language: | English |

Subject: | Markov processes. Measure theory. MATHEMATICS -- Probability & Statistics -- Stochastic Processes. Markov processes. Measure theory. Mathematical Statistics. Mathematics. Physical Sciences & Mathematics. Electronic books. Electronic books. |

Format: | E-Resource Book |

URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11214025 |

**Table of Contents:**

- 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.