Exercises and Solutions Manual for Integration and Probability
Exercises and Solutions Manual for Integration and Probability

Author: Paul Malliavin

Publisher: Springer Science & Business Media

Published: 1995-06-13

Total Pages: 158

ISBN-13: 9780387944210

DOWNLOAD EBOOK

This book is designed to be an introduction to analysis with the proper mix of abstract theories and concrete problems. It starts with general measure theory, treats Borel and Radon measures (with particular attention paid to Lebesgue measure) and introduces the reader to Fourier analysis in Euclidean spaces with a treatment of Sobolev spaces, distributions, and the Fourier analysis of such. It continues with a Hilbertian treatment of the basic laws of probability including Doob's martingale convergence theorem and finishes with Malliavin's "stochastic calculus of variations" developed in the context of Gaussian measure spaces. This invaluable contribution to the existing literature gives the reader a taste of the fact that analysis is not a collection of independent theories but can be treated as a whole.

Exercises and Solutions Manual for Integration and Probability
Exercises and Solutions Manual for Integration and Probability

Author: Gerard Letac

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 147

ISBN-13: 1461242126

DOWNLOAD EBOOK

This book presents the problems and worked-out solutions for all the exercises in the text by Malliavin. It will be of use not only to mathematics teachers, but also to students using the text for self-study.

A First Look at Rigorous Probability Theory
A First Look at Rigorous Probability Theory

Author: Jeffrey Seth Rosenthal

Publisher: World Scientific

Published: 2006

Total Pages: 238

ISBN-13: 9812703705

DOWNLOAD EBOOK

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.

Exercises in Probability
Exercises in Probability

Author: L. Chaumont

Publisher: Cambridge University Press

Published: 2003-11-03

Total Pages: 256

ISBN-13: 0521825857

DOWNLOAD EBOOK

This book was first published in 2003. Derived from extensive teaching experience in Paris, this book presents around 100 exercises in probability. The exercises cover measure theory and probability, independence and conditioning, Gaussian variables, distributional computations, convergence of random variables, and random processes. For each exercise the authors have provided detailed solutions as well as references for preliminary and further reading. There are also many insightful notes to motivate the student and set the exercises in context. Students will find these exercises extremely useful for easing the transition between simple and complex probabilistic frameworks. Indeed, many of the exercises here will lead the student on to frontier research topics in probability. Along the way, attention is drawn to a number of traps into which students of probability often fall. This book is ideal for independent study or as the companion to a course in advanced probability theory.

Exercises in Probability
Exercises in Probability

Author: Loïc Chaumont

Publisher: Cambridge University Press

Published: 2012-07-19

Total Pages: 301

ISBN-13: 1107606551

DOWNLOAD EBOOK

Over 100 exercises with detailed solutions, insightful notes and references for further reading. Ideal for beginning researchers.

Measure, Integral and Probability
Measure, Integral and Probability

Author: Marek Capinski

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 229

ISBN-13: 1447136314

DOWNLOAD EBOOK

This very well written and accessible book emphasizes the reasons for studying measure theory, which is the foundation of much of probability. By focusing on measure, many illustrative examples and applications, including a thorough discussion of standard probability distributions and densities, are opened. The book also includes many problems and their fully worked solutions.

Probability and Stochastic Processes
Probability and Stochastic Processes

Author: Roy D. Yates

Publisher: John Wiley & Sons

Published: 2014-01-28

Total Pages: 514

ISBN-13: 1118324560

DOWNLOAD EBOOK

This text introduces engineering students to probability theory and stochastic processes. Along with thorough mathematical development of the subject, the book presents intuitive explanations of key points in order to give students the insights they need to apply math to practical engineering problems. The first five chapters contain the core material that is essential to any introductory course. In one-semester undergraduate courses, instructors can select material from the remaining chapters to meet their individual goals. Graduate courses can cover all chapters in one semester.

Introduction to Probability
Introduction to Probability

Author: Joseph K. Blitzstein

Publisher: CRC Press

Published: 2014-07-24

Total Pages: 599

ISBN-13: 1466575573

DOWNLOAD EBOOK

Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

Introduction to Probability
Introduction to Probability

Author: Dimitri Bertsekas

Publisher: Athena Scientific

Published: 2008-07-01

Total Pages: 544

ISBN-13: 188652923X

DOWNLOAD EBOOK

An intuitive, yet precise introduction to probability theory, stochastic processes, statistical inference, and probabilistic models used in science, engineering, economics, and related fields. This is the currently used textbook for an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students, and for a leading online class on the subject. The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains a number of more advanced topics, including transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics. The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis is explained intuitively in the main text, and then developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems.

Measures, Integrals and Martingales
Measures, Integrals and Martingales

Author: René L. Schilling

Publisher: Cambridge University Press

Published: 2005-11-10

Total Pages: 404

ISBN-13: 9780521850155

DOWNLOAD EBOOK

This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability.