Random and vector measures - Rao, M. M., (Malempati Madhusudana) (World Scientific, 2012)
Includes bibliographical references (p. [497]-521) and index
1. Introduction and motivation. 1.1. Introducing vector valued measures. 1.2. Basic structures. 1.3. Additivity properties of vector valued measures. 1.4. Complements and exercises -- 2. Second order random measures and representations. 2.1. Introduction. 2.2. Structures of second order random measures. 2.3. Shift invariant second order random measures. 2.4. A specialization of random measures invariant on subgroups. 2.5. Complements and exercises -- 3. Random measures admitting controls. 3.1. Structural analysis. 3.2. Controls for weakly stable random measures. 3.3. Integral representations of stable classes by random measures. 3.4. Integral representations of some second order processes. 3.5. Complements and exercises --
- 4. Random measures in Hilbert space : specialized analysis. 4.1. Bilinear functionals associated with random measures. 4.2. Local classes of random fields and related measures. 4.3. Bilinear forms and random measures. 4.4. Random measures with constraints. 4.5. Complements and exercises -- 5. More on random measures and integrals. 5.1. Random measures, bimeasures and convolutions. 5.2. Bilinear forms and random measure algebras. 5.3. Vector integrands and integrals with stable random measures. 5.4. Positive and other special classes of random measures. 5.5. Complements and exercises -- 6. Martingale type measures and their integrals. 6.1. Random measures and deterministic integrands. 6.2. Random measures and stochastic integrands. 6.3. Random measures, stopping times and stochastic integration. 6.4. Generalizations of Martingale integrals. 6.5. Complements and exercises --
- 7. Multiple random measures and integrals. 7.1. Basic quasimartingale spaces and integrals. 7.2. Multiple random measures, Part I : Cartesian products. 7.3. Multiple random measures, Part II :Noncartesian products. 7.4. Random line integrals with Fubini and Green-Stokes theorems. 7.5. Random measures on partially ordered sets. 7.6. Multiple random integrals using white noise methods. 7.7. Complements and exercises -- 8. Vector measures and integrals. 8.1. Vector measures of nonfinite variation. 8.2. Vector integration with measures of finite semivariation, Part I. 8.3. Vector integration with measures of finite semivariation, Part II. 8.4. Some applications of vector measure integration, Part I. 8.5. Some applications of vector measure integration, Part II. 8.6. Complements and exercises --
- 9. Random and vector multimeasures. 9.1. Bimeasures and multiple integrals. 9.2. Bimeasure domination, dilations and representations of processes. 9.3. Spectral analysis of second order fields and bimeasures. 9.4. Multimeasures and multilinear forms. 9.5. Complements and exercises