Cambridge series in statistical and probabilistic mathematics
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
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Includes bibliographical references and index
CONTENTS NOTE
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Chapter 1. Motivation -- Ch. 2. A modicum of measure theory -- Ch. 3. Densities and derivatives -- Ch. 4. Product spaces and independence -- Ch. 5. Conditioning -- Ch. 6. Martingale et al. -- Ch. 7. Convergence in distribution -- Ch. 8. Fourier transforms -- Ch. 9. Brownian motion -- Ch. 10. Representations and couplings -- Ch. 11. Exponential tails and the law of the iterated logarithm -- Ch. 12. Multivariate normal distributions -- App. A. Measures and integrals -- App. B. Hilbert spaces -- App. C. Convexity -- App. D. Binomial and normal distributions -- App. E. Martingales in continuous time -- App. F. Disintegration of measures
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SUMMARY OR ABSTRACT
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This text is not just a presentation of mathematical theory, but also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguements and understand what they mean