{"product_id":"a-users-guide-to-measure-theoretic-probability-hardback-9780521802420","title":"A User's Guide to Measure Theoretic Probability (Hardback) 9780521802420","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eA User's Guide to Measure Theoretic Probability\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThis 2002 book is a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDavid Pollard (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521802420, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 17 December 2001\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e366 pages, 200 exercises\u003cbr\u003e25.4 x 17.8 x 2.1 cm, 0.85 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'A really useful book …'. EMS Newsletter\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eRigorous probabilistic arguments, built on the foundation of measure theory introduced eighty years ago by Kolmogorov, have invaded many fields. Students of statistics, biostatistics, econometrics, finance, and other changing disciplines now find themselves needing to absorb theory beyond what they might have learned in the typical undergraduate, calculus-based probability course. This 2002 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Motivation\u003cbr\u003e 2. A modicum of measure theory\u003cbr\u003e 3. Densities and derivatives\u003cbr\u003e 4. Product spaces and independence\u003cbr\u003e 5. Conditioning\u003cbr\u003e 6. Martingale et al\u003cbr\u003e 7. Convergence in distribution\u003cbr\u003e 8. Fourier transforms\u003cbr\u003e 9. Brownian motion\u003cbr\u003e 10. Representations and couplings\u003cbr\u003e 11. Exponential tails and the law of the iterated logarithm\u003cbr\u003e 12. Multivariate normal distributions\u003cbr\u003e Appendix A. Measures and integrals\u003cbr\u003e Appendix B. Hilbert spaces\u003cbr\u003e Appendix C. Convexity\u003cbr\u003e Appendix D. Binomial and normal distributions\u003cbr\u003e Appendix E. Martingales in continuous time\u003cbr\u003e Appendix F. Generalized sequences.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Probability \u0026amp; statistics [\u003ca title=\"See our other books on Probability \u0026amp; statistics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Probability%20\u0026amp;%20statistics%20%5BPBT%5D%22\"\u003ePBT\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46004689568024,"sku":"9780521802420","price":119.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521802420i_33a25d3e-2d67-44f8-8804-3e55fc6931d4.jpg?v=1691368191","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/a-users-guide-to-measure-theoretic-probability-hardback-9780521802420","provider":"Freshly Printed Books","version":"1.0","type":"link"}