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Stopping times and directed processes /
The notion of 'stopping times' is a useful one in probability theory; it can be applied to both classical problems and fresh ones. This book presents this technique in the context of the directed set, stochastic processes indexed by directed sets, and many applications in probability, anal...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [England] ; New York, NY, USA :
Cambridge University Press,
1992.
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| Colección: | Encyclopedia of mathematics and its applications ;
v. 47. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Half-title; Title; Copyright; Contents; Preface; 1. Stopping times; 1.1. Definitions; Directed sets; Stochastic basis; Stopping times; Optional stopping; Complements; 1.2. The amart convergence theorem; The lattice property; Convergence; Complements; 1.3. Directed processes and the Radon-Nikodym theorem; Processes indexed by directed sets; Complements; 1.4. Conditional expectations; Definition and basic properties; Martingales and related processes; Riesz decomposition; The sequential case; Complements; 2. Infinite measure and Orlicz spaces; 2.1. Orlicz spaces
- Orlicz functions and their conjugatesOrlicz spaces; Complements; 2.2. More on Orlicz spaces; Comparison of orlicz spaces; Largest and smallest orlicz functions; Duality for orlicz spaces; 2.3. Uniform integrability and conditional expectation; Conditional expectation in infinite measure spaces; Complements; 3. Inequalities; 3.1. The three-function inequality; Complements; 3.2. Sharp maximal inequality for martingale transforms; 3.3. Prophet compared to gambler; Stopped processes; Transformed processes; The case of signed U; Complements; Remarks; 4. Directed index set
- 5.2. Martingales and amartsElementary properties; Complements; 5.3. The Radon-Nikodým property; Scalar and pettis norm convergence; Weak a.s. convergence; Strong convergence; T-convergence; Converses; Complements; 5.4. Geometric properties; The choquet-edgar theorem; Common fixed points for noncommuting maps; Dentability; Strongly exposed points; Complements; Remarks; 5.5. Operator ideals; Absolutely summing operators; Radon-nikodym operators; Asplund operators; Complements; 6. Martingales; 6.1. Maximal inequalities for supermartingales; A maximal inequality; A law of large numbers