Random Series and Stochastic Integrals: Single and Multiple
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Random Series and Stochastic Integrals: Single and Multiple: Single and Multiple(Probability and Its Applications)

Random Series and Stochastic Integrals: Single and Multiple: Single and Multiple(Probability and Its Applications)


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About the Book

This volume studies the foundations of the theory of linear and nonlinear forms in single and multiple random variables including single and multiple random series and stochastic integrals, both Gaussian and non-Gaussian. Its topic is intimately connected with a number of classical problems of probability theory such as the summation of independent random variables, martingale theory and the Weiner theory of polynomial chaos, as well as with several application areas such as stochastic analysis, limit theorems for symmetric statistics, representation of random fields, partial differential equations and quantum field theory. The emphasis is on domination principles for comparison of sequences of random variables and on decoupling techniques. The volume is intended for researchers and graduate students in probability theory, stochastic processes, theoretical statistics and in several areas of theoretical physics and engineering.

Table of Contents:
0 Preliminaries.- 0.1 Topology and measures.- 0.2 Tail inequalities.- 0.3 Filtrations and stopping times.- 0.4 Extensions of probability spaces.- 0.5 Bernoulli and canonical Gaussian and ?-stable sequences.- 0.6 Gaussian measures on linear spaces.- 0.7 Modulars on linear spaces.- 0.8 Musielak-Orlicz spaces.- 0.9 Random Musielak-Orlicz spaces.- 0.10 Complements and comments.- Bibliographical notes.- I Random Series.- 1 Basic Inequalities for Random Linear Forms in Independent Random Variables.- 2 Convergence of Series of Independent Random Variables.- 3 Domination Principles and Comparison of Sums of Independent Random Variables.- 4 Martingales.- 5 Domination Principles for Martingales.- 6 Random Multilinear Forms in Independent Random Variables and Polynomial Chaos.- II Stochastic Integrals.- 7 Integration with Respect to General Stochastic Measures.- 8 Deterministic Integrands.- 9 Predictable Integrands.- 10 Multiple Stochastic Integrals.- A Unconditional and Bounded Multiplier Convergence of Random Series.- A.2 Almost sure convergence.- A.3 Complements and comments.- A hypercontractive view.- Bibliographical notes.- B Vector Measures.- B.1 Extensions of vector measures.- B.2 Boundedness and control measure of stochastic measures.- B.3 Complements and comments.- Bibliographical notes.


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Product Details
  • ISBN-13: 9780817641986
  • Publisher: Birkhauser Boston Inc
  • Publisher Imprint: Birkhauser Boston Inc
  • Edition: New edition
  • No of Pages: 360
  • Returnable: Y
  • Sub Title: Single and Multiple
  • ISBN-10: 081764198X
  • Publisher Date: 11 May 2000
  • Binding: Paperback
  • Language: English
  • Returnable: Y
  • Series Title: Probability and Its Applications


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Random Series and Stochastic Integrals: Single and Multiple: Single and Multiple(Probability and Its Applications)
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