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Home > Mathematics and Science Textbooks > Mathematics > Algebra > Random and Vector Measures: Theory and Applications(Probability and Its Applications)
Random and Vector Measures: Theory and Applications(Probability and Its Applications)

Random and Vector Measures: Theory and Applications(Probability and Its Applications)


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About the Book

This comprehensive text treats the complementary subjects of random and vector measures. A vector-valued measure is a function on a ring of sets taking values in a vector space, and a random measure is a subclass of vector measures whose value spaces are built on a probability space. There is a common foundation for both, yet each has different application potentials. The book examines the representations of random and vector measures, random measures on probability (i.e., Frechet, Banach, and Hilbert) spaces, the bimeasures associated with random measures and the extension to polymeasures, boundedness principles, and the importance of random and vector measures in applications. The interaction between random and vector measures is explained, thus helping to understand the deeper aspects of vector-valued analysis. This comparative and distinctive text is ideal for either graduate students in the classroom setting, or for researchers in mathematics, statistics, and engineering.

Table of Contents:
Introduction and motivation.-Second order random measures and their representations.-Random measures admitting controls.-Random measures in Banach spaces and their integrals.-Stable random measures in Frechet spaces and integrals.-Vector measures on d-rings and their use in integral representations of vector functions.-Bimeasures associated with random measures and extensions to polymeasures.-Integral representations of random processes by vector measures.-Random measures and stable stochastic integrals.-Martingale measures and applications.-Generalized Poisson measures and counting processes.-Applications to random (trigonometric) series.-Multiple random integrals and measures.-Chaos (Hida-) expansions and summability.-Abstract Wiener integral and its analysis.-References.-Index.


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Product Details
  • ISBN-13: 9780817645175
  • Publisher: Birkhauser Boston Inc
  • Publisher Imprint: Birkhauser Boston Inc
  • Series Title: Probability and Its Applications
  • ISBN-10: 0817645179
  • Publisher Date: /05/2009
  • Binding: Hardback
  • Sub Title: Theory and Applications


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