Probability with a View Towards Statistics, Two Volume Set

ISBN-13: 9780412054211 / Angielski / Twarda / 1994 / 1122 str.

J. Hoffmann-Jorgensen

Opis

Volume I of this two-volume text and reference work begins by providing a foundation in measure and integration theory. It then offers a systematic introduction to probability theory, and in particular, those parts that are used in statistics. This volume discusses the law of large numbers for independent and non-independent random variables, transforms, special distributions, convergence in law, the central limit theorem for normal and infinitely divisible laws, conditional expectations and martingales. Unusual topics include the uniqueness and convergence theorem for general transforms with characteristic functions, Laplace transforms, moment transforms and generating functions as special examples. The text contains substantive applications, e.g., epidemic models, the ballot problem, stock market models and water reservoir models, and discussion of the historical background. The exercise sets contain a variety of problems ranging from simple exercises to extensions of the theory.

Spis treści

Volume I – Measure Theory, Probability Measures, Integration, Expectations and Moments, Convergence in Law, Conditional Expectations, Martingales, Prerequisites. Volume II - Random vectors and their densities; Stochastic processes; Regular conditional probabilities; Optimal stopping strategies; Exponential families; Consistency of maximum estimators; Asymptotic normality; Exercises; Prerequisites.

O autorze

J. Hoffman-Jorgensen (University of Aarhus, Denmark) (Author)