Handbook of Probability

Front Cover
John Wiley & Sons, Oct 28, 2013 - Mathematics - 472 pages

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.

 

Selected pages

Contents

Introduction
Exercises
Random Variables The Discrete Case
Random Variables The Continuous Case
Generating Random Variables
Exercises
Characteristic Function
Distributions
Gaussian Random Vectors
Exercises
Limit Theorems
Appendix A Integration Theory General Expectations
Appendix B Inequalities Involving Random Variables
Bibliography
Copyright

Common terms and phrases

algebra apply balls Bernoulli calculate change of variables chapter characteristic function components compute constant continuous random variables convergence in distribution convergence in probability countable covariance matrix cumulative distribution function defined definition denote density f discrete random variables distributed random variables distribution with parameters eigenvalues estimator Example exercise exists expectation exponential distribution Find finite formula function f Gaussian random variables Gaussian vector given i.i.d. random variables implies importance sampling independent random variables inequality integral interval inverse large numbers Lemma Let X1 marginal distributions mean measurable function moment-generating function normal distribution normal random variables notation Note o-algebra obtain outcomes positive probability density function probability distribution probability measure probability space probability theory problem Proof Proposition prove random numbers random vector Recall Remark result sequence of random sequence Xn Show Solution subset Suppose uniform distribution variable with density variance

About the author (2013)

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.

Bibliographic information

TitleHandbook of Probability
Wiley Handbooks in Applied Statistics
AuthorsIonut Florescu, Ciprian A. Tudor
Editionillustrated
PublisherJohn Wiley & Sons, 2013
ISBN111859309X, 9781118593097
Length472 pages
Subjects ›  › 

Mathematics / Applied
Mathematics / General
Mathematics / Probability & Statistics / General
Mathematics / Probability & Statistics / Stochastic Processes
Mathematics / Reference
  
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