An
Intermediate Course in Probability
Gut, Allan.
creator
author.
SpringerLink (Online service)
text
xxu
2009
monographic
eng
access
XV, 303 p. online resource.
The purpose of this book is to provide the reader with a solid background and understanding of the basic results and methods in probability theory before entering into more advanced courses. The first six chapters focus on some central areas of what might be called pure probability theory: multivariate random variables, conditioning, transforms, order variables, the multivariate normal distribution, and convergence. A final chapter is devoted to the Poisson process as a means both to introduce stochastic processes and to apply many of the techniques introduced earlier in the text. Students are assumed to have taken a first course in probability, though no knowledge of measure theory is assumed. Throughout, the presentation is thorough and includes many examples that are discussed in detail. Thus, students considering more advanced research in probability theory will benefit from this wide-ranging survey of the subject that provides them with a foretaste of the subject's many treasures. The present second edition offers updated content, one hundred additional problems for solution, and a new chapter that provides an outlook on further areas and topics, such as stable distributions and domains of attraction, extreme value theory and records, and martingales. The main idea is that this chapter may serve as an appetizer to the more advanced theory. Allan Gut is Professor of Mathematical Statistics at Uppsala University, Uppsala, Sweden. He is a member of the International Statistical Institute, the Bernoulli Society, the Institute of Mathematical Statistics, and the Swedish Statistical Society. He is an Associate Editor of the Journal of Statistical Planning and Inference and Sequential Analysis, a former Associate Editor of the Scandinavian Journal of Statistics, and the author of five other books including Probability: A Graduate Course (Springer, 2005) and Stopped Random Walks: Limit Theorems and Applications, Second Edition (Springer, 2009).
Multivariate Random Variables -- Conditioning -- Transforms -- Order Statistics -- The Multivariate Normal Distribution -- Convergence -- An Outlook on Further Topics -- The Poisson Process.
by Allan Gut.
Mathematics
Computers
Mathematical statistics
Life sciences
Probabilities
Statistics
Environmental sciences
Mathematics
Probability Theory and Stochastic Processes
Life Sciences, general
Theory of Computation
Statistical Theory and Methods
Probability and Statistics in Computer Science
Math. Appl. in Environmental Science
QA273.A1-274.9
QA274-274.9
519.2
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