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Author: David Pollard Publisher: Cambridge University Press ISBN: 9780521002899 Category : Mathematics Languages : en Pages : 372
Book Description
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.
Author: David Pollard Publisher: Cambridge University Press ISBN: 9780521002899 Category : Mathematics Languages : en Pages : 372
Book Description
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.
Author: David Pollard Publisher: Cambridge University Press ISBN: 1139936530 Category : Mathematics Languages : en Pages : 375
Book Description
Rigorous 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.
Author: George G. Roussas Publisher: Gulf Professional Publishing ISBN: 0125990227 Category : Computers Languages : en Pages : 463
Book Description
This book provides in a concise, yet detailed way, the bulk of the probabilistic tools that a student working toward an advanced degree in statistics, probability and other related areas, should be equipped with. The approach is classical, avoiding the use of mathematical tools not necessary for carrying out the discussions. All proofs are presented in full detail. * Excellent exposition marked by a clear, coherent and logical devleopment of the subject * Easy to understand, detailed discussion of material * Complete proofs
Author: Malcolm Adams Publisher: Springer Science & Business Media ISBN: 1461207797 Category : Mathematics Languages : en Pages : 217
Book Description
"...the text is user friendly to the topics it considers and should be very accessible...Instructors and students of statistical measure theoretic courses will appreciate the numerous informative exercises; helpful hints or solution outlines are given with many of the problems. All in all, the text should make a useful reference for professionals and students."—The Journal of the American Statistical Association
Author: Seán Dineen Publisher: American Mathematical Soc. ISBN: 0821894900 Category : Mathematics Languages : en Pages : 323
Book Description
The use of the Black-Scholes model and formula is pervasive in financial markets. There are very few undergraduate textbooks available on the subject and, until now, almost none written by mathematicians. Based on a course given by the author, the goal of
Author: Robert B. Ash Publisher: Academic Press ISBN: 9780120652020 Category : Mathematics Languages : en Pages : 536
Book Description
Probability and Measure Theory, Second Edition, is a text for a graduate-level course in probability that includes essential background topics in analysis. It provides extensive coverage of conditional probability and expectation, strong laws of large numbers, martingale theory, the central limit theorem, ergodic theory, and Brownian motion. Clear, readable style Solutions to many problems presented in text Solutions manual for instructors Material new to the second edition on ergodic theory, Brownian motion, and convergence theorems used in statistics No knowledge of general topology required, just basic analysis and metric spaces Efficient organization
Author: Jeffrey Seth Rosenthal Publisher: World Scientific ISBN: 9812703705 Category : Mathematics Languages : en Pages : 238
Book Description
Features an introduction to probability theory using measure theory. This work provides proofs of the essential introductory results and presents the measure theory and mathematical details in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects.
Author: Patrick Billingsley Publisher: John Wiley & Sons ISBN: 9788126517718 Category : Languages : en Pages : 612
Book Description
Now in its new third edition, Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining the unique approach of the previous editions, this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory and measure theory is then developed and applied to probability. Probability and Measure provides thorough coverage of probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes. The Third Edition features an improved treatment of Brownian motion and the replacement of queuing theory with ergodic theory.· Probability· Measure· Integration· Random Variables and Expected Values· Convergence of Distributions· Derivatives and Conditional Probability· Stochastic Processes
Author: Santosh S. Venkatesh Publisher: Cambridge University Press ISBN: 1107024471 Category : Mathematics Languages : en Pages : 830
Book Description
From classical foundations to modern theory, this comprehensive guide to probability interweaves mathematical proofs, historical context and detailed illustrative applications.
Author: David Pollard
Author: David Pollard
Author: David Pollard
Author: Ross Leadbetter
Author: George G. Roussas
Author: Malcolm Adams
Author: Seán Dineen
Author: Robert B. Ash
Author: Jeffrey Seth Rosenthal
Author: Patrick Billingsley
Author: Santosh S. Venkatesh