Lower previsions /
| Κύριος συγγραφέας: | |
|---|---|
| Άλλοι συγγραφείς: | |
| Μορφή: | Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
Chichester, West Sussex, United Kingdom :
Wiley,
2014.
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| Σειρά: | Wiley series in probability and statistics.
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| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- Wiley Series in Probability and Statistics; Title Page; Copyright; Dedication; Preface; Acknowledgements; Chapter 1: Preliminary notions and definitions; 1.1 Sets of numbers; 1.2 Gambles; 1.3 Subsets and their indicators; 1.4 Collections of events; 1.5 Directed sets and Moore-Smith limits; 1.6 Uniform convergence of bounded gambles; 1.7 Set functions, charges and measures; 1.8 Measurability and simple gambles; 1.9 Real functionals; 1.10 A useful lemma; Part I: Lower Previsions on Bounded Gambles; Chapter 2: Introduction; Chapter 3: Sets of acceptable bounded gambles; 3.1 Random variables
- 3.2 Belief and behaviour3.3 Bounded gambles; 3.4 Sets of acceptable bounded gambles; Chapter 4: Lower previsions; 4.1 Lower and upper previsions; 4.2 Consistency for lower previsions; 4.3 Coherence for lower previsions; 4.4 Properties of coherent lower previsions; 4.5 The natural extension of a lower prevision; 4.6 Alternative characterisations for avoiding sure loss, coherence, and natural extension; 4.7 Topological considerations; Chapter 5: Special coherent lower previsions; 5.1 Linear previsions on finite spaces; 5.2 Coherent lower previsions on finite spaces
- 5.3 Limits as linear previsions5.4 Vacuous lower previsions; 5.5 {0,1}-valued lower probabilities; Chapter 6: n-Monotone lower previsions; 6.1 n-Monotonicity; 6.2 n-Monotonicity and coherence; 6.3 Representation results; Chapter 7: Special n-monotone coherent lower previsions; 7.1 Lower and upper mass functions; 7.2 Minimum preserving lower previsions; 7.3 Belief functions; 7.4 Lower previsions associated with proper filters; 7.5 Induced lower previsions; 7.6 Special cases of induced lower previsions; 7.7 Assessments on chains of sets; 7.8 Possibility and necessity measures
- 7.9 Distribution functions and probability boxesChapter 8: Linear previsions, integration and duality; 8.1 Linear extension and integration; 8.2 Integration of probability charges; 8.3 Inner and outer set function, completion and other extensions; 8.4 Linear previsions and probability charges; 8.5 The S-integral; 8.6 The Lebesgue integral; 8.7 The Dunford integral; Chapter 9: Examples of linear extension; 9.1 Distribution functions; 9.2 Limits inferior; 9.3 Lower and upper oscillations; 9.4 Linear extension of a probability measure
- 9.5 Extending a linear prevision from continuous bounded gambles9.6 Induced lower previsions and random sets; Chapter 10: Lower previsions and symmetry; 10.1 Invariance for lower previsions; 10.2 An important special case; 10.3 Interesting examples; Chapter 11: Extreme lower previsions; 11.1 Preliminary results concerning real functionals; 11.2 Inequality preserving functionals; 11.3 Properties of inequality preserving functionals; 11.4 Infinite non-negative linear combinations of inequality preserving functionals; 11.5 Representation results
