Handbook of Probability

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THE COMPLETE COLLECTION NECESSARY FOR A CONCRETE UNDERSTANDING OF PROBABILITY

Written in a clear, accessible, and comprehensive manner, the Handbook of Probability presents the fundamentals of probability with an emphasis on the balance of theory, application, and methodology. Utilizing basic examples throughout, the handbook expertly transitions between concepts and practice to allow readers an inclusive introduction to the field of probability.


The book provides a useful format with self-contained chapters, allowing the reader easy and quick reference. Each chapter includes an introduction, historical background, theory and applications, algorithms, and exercises. The Handbook of Probability offers coverage of:

  • Probability Space
  • Probability Measure
  • Random Variables
  • Random Vectors in Rn
  • Characteristic Function
  • Moment Generating Function
  • Gaussian Random Vectors
  • Convergence Types
  • Limit Theorems

The Handbook of Probability is an ideal resource for researchers and practitioners in numerous fields, such as mathematics, statistics, operations research, engineering, medicine, and finance, as well as a useful text for graduate students.

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About the author

IONUT FLORESCU, PhD, is Research Associate Professor of Financial Engineering and Director of the Hanlon Financial Systems Lab at Stevens Institute of Technology. He has published extensively in his areas of research interest, which include stochastic volatility, stochastic partial differential equations, Monte Carlo methods, and numerical methods for stochastic processes.

CIPRIAN A. TUDOR, PhD, is Professor of Mathematics at the University of Lille 1, France. His research interests include Brownian motion, limit theorems, statistical inference for stochastic processes, and financial mathematics. He has over eighty scientific publications in various internationally recognized journals on probability theory and statistics. He serves as a referee for over a dozen journals and has spoken at more than thirty-five conferences worldwide.

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Additional Information

Publisher
John Wiley & Sons
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Published on
Oct 28, 2013
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Pages
472
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ISBN
9781118593097
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Language
English
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Genres
Mathematics / Applied
Mathematics / Probability & Statistics / General
Mathematics / Probability & Statistics / Stochastic Processes
Mathematics / Reference
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Content Protection
This content is DRM protected.
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Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains. A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit theorem. There is an account of moment generating functions and their applications. The following three chapters are about branching processes, random walks, and continuous-time random processes such as the Poisson process. The final chapter is a fairly extensive account of Markov chains in discrete time. This second edition develops the success of the first edition through an updated presentation, the extensive new chapter on Markov chains, and a number of new sections to ensure comprehensive coverage of the syllabi at major universities.
A comprehensive and accessible presentation of probability and stochastic processes with emphasis on key theoretical concepts and real-world applications

With a sophisticated approach, Probability and Stochastic Processes successfully balances theory and applications in a pedagogical and accessible format. The book’s primary focus is on key theoretical notions in probability to provide a foundation for understanding concepts and examples related to stochastic processes.

Organized into two main sections, the book begins by developing probability theory with topical coverage on probability measure; random variables; integration theory; product spaces, conditional distribution, and conditional expectations; and limit theorems. The second part explores stochastic processes and related concepts including the Poisson process, renewal processes, Markov chains, semi-Markov processes, martingales, and Brownian motion. Featuring a logical combination of traditional and complex theories as well as practices, Probability and Stochastic Processes also includes:

Multiple examples from disciplines such as business, mathematical finance, and engineering Chapter-by-chapter exercises and examples to allow readers to test their comprehension of the presented material A rigorous treatment of all probability and stochastic processes concepts
An appropriate textbook for probability and stochastic processes courses at the upper-undergraduate and graduate level in mathematics, business, and electrical engineering, Probability and Stochastic Processes is also an ideal reference for researchers and practitioners in the fields of mathematics, engineering, and finance.
An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance to marketing to astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines, clustering, and more. Color graphics and real-world examples are used to illustrate the methods presented. Since the goal of this textbook is to facilitate the use of these statistical learning techniques by practitioners in science, industry, and other fields, each chapter contains a tutorial on implementing the analyses and methods presented in R, an extremely popular open source statistical software platform.

Two of the authors co-wrote The Elements of Statistical Learning (Hastie, Tibshirani and Friedman, 2nd edition 2009), a popular reference book for statistics and machine learning researchers. An Introduction to Statistical Learning covers many of the same topics, but at a level accessible to a much broader audience. This book is targeted at statisticians and non-statisticians alike who wish to use cutting-edge statistical learning techniques to analyze their data. The text assumes only a previous course in linear regression and no knowledge of matrix algebra.

CUTTING-EDGE DEVELOPMENTS IN HIGH-FREQUENCY FINANCIAL ECONOMETRICS

In recent years, the availability of high-frequency data and advances in computing have allowed financial practitioners to design systems that can handle and analyze this information. Handbook of Modeling High-Frequency Data in Finance addresses the many theoretical and practical questions raised by the nature and intrinsic properties of this data.

A one-stop compilation of empirical and analytical research, this handbook explores data sampled with high-frequency finance in financial engineering, statistics, and the modern financial business arena. Every chapter uses real-world examples to present new, original, and relevant topics that relate to newly evolving discoveries in high-frequency finance, such as:

Designing new methodology to discover elasticity and plasticity of price evolution

Constructing microstructure simulation models

Calculation of option prices in the presence of jumps and transaction costs

Using boosting for financial analysis and trading

The handbook motivates practitioners to apply high-frequency finance to real-world situations by including exclusive topics such as risk measurement and management, UHF data, microstructure, dynamic multi-period optimization, mortgage data models, hybrid Monte Carlo, retirement, trading systems and forecasting, pricing, and boosting. The diverse topics and viewpoints presented in each chapter ensure that readers are supplied with a wide treatment of practical methods.

Handbook of Modeling High-Frequency Data in Finance is an essential reference for academics and practitioners in finance, business, and econometrics who work with high-frequency data in their everyday work. It also serves as a supplement for risk management and high-frequency finance courses at the upper-undergraduate and graduate levels.

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