This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The…mehr
This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is 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 arguments and understand what they mean.
David Pollard nació en 1942 y ha sido vendedor de muebles, contable, profesor de inglés para extranjeros y profesor universitario. Obtuvo sus tres títulos de la Universidad de Sussex y desde entonces ha enseñado en las universidades de Sussex, Essex y la Universidad Hebrea de Jerusalén, donde fue Lady Davis Scholar. Ha publicado The Poetry of Keats: Language and Experience que fue su tesis doctoral, A KWIC Concordance to The Harvard Edition of The Letters of John Keats, una novela, Nietzsche's Footfalls y siete volúmenes de poesía: patricides, Risk of Skin, bedbound, Self-Portraits, Finis-terre, Three Artists y Broken Voices. También ha publicado en otros medios, como antologías especializadas y revistas de poesía. Divide su tiempo entre Hove, en el sur de Inglaterra, y Beluso, en Galicia. La edición en inglés de Finis-terre (2015) fue merecedora de una Poetry Book Society Recommendation.
Inhaltsangabe
1. Motivation 2. A modicum of measure theory 3. Densities and derivatives 4. Product spaces and independence 5. Conditioning 6. Martingale et al 7. Convergence in distribution 8. Fourier transforms 9. Brownian motion 10. Representations and couplings 11. Exponential tails and the law of the iterated logarithm 12. Multivariate normal distributions Appendix A. Measures and integrals Appendix B. Hilbert spaces Appendix C. Convexity Appendix D. Binomial and normal distributions Appendix E. Martingales in continuous time Appendix F. Generalized sequences.
1. Motivation 2. A modicum of measure theory 3. Densities and derivatives 4. Product spaces and independence 5. Conditioning 6. Martingale et al 7. Convergence in distribution 8. Fourier transforms 9. Brownian motion 10. Representations and couplings 11. Exponential tails and the law of the iterated logarithm 12. Multivariate normal distributions Appendix A. Measures and integrals Appendix B. Hilbert spaces Appendix C. Convexity Appendix D. Binomial and normal distributions Appendix E. Martingales in continuous time Appendix F. Generalized sequences.
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