Best probability chung list
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Best probability chung
1. A Course in Probability Theory, Third Edition
Description
Since the publication of the first edition of this classic textbook over thirty years ago, tens of thousands of students have used A Course in Probability Theory. New in this edition is an introduction to measure theory that expands the market, as this treatment is more consistent with current courses.
While there are several books on probability, Chung's book is considered a classic, original work in probability theory due to its elite level of sophistication.
2. A Course in Probability Theory, Second Edition (Probability and Mathematical Statistics, 21)
Description
This book contains about 500 exercises consisting mostly of special cases and examples, second thoughts and alternative arguments, natural extensions, and some novel departures. With a few obvious exceptions they are neither profound nor trivial, and hints and comments are appended to many of them. If they tend to be somewhat inbred, at least they are relevant to the text and should help in its digestion. As a bold venture I have marked a few of them with a * to indicate a "must", although no rigid standard of selection has been used. Some of these are needed in the book, but in any case the reader's study of the text will be more complete after he has tried at least those problems.3. Green, Brown, & Probability and Brownian Motion on the Line
Description
This invaluable book consists of two parts. Part I is the second edition of the author's widely acclaimed publication Green, Brown, and Probability, which first appeared in 1995. In this exposition the author reveals, from a historical perspective, the beautiful relations between the Brownian motion process in probability theory and two important aspects of the theory of partial differential equations initiated from the problems in electricity Green's formula for solving the boundary value problem of Laplace equations and the Newton-Coulomb potential.Part II of the book comprises lecture notes based on a short course on Brownian Motion on the Line which the author has given to graduate students at Stanford University. It emphasizes the methodology of Brownian motion in the relatively simple case of one-dimensional space. Numerous exercises are included.4. Markov Chains: With Stationary Transition Probabilities (Grundlehren der mathematischen Wissenschaften)
Description
From the reviews:J. Neveu, 1962 in Zentralblatt fr Mathematik, 92.Band Heft 2, p. 343: "Ce livre crit par l'un des plus minents spcialistes en la matire, est un expos trs dtaill de la thorie des processus de Markov dfinis sur un espace dnombrable d'tats et homognes dans le temps (chaines stationnaires de Markov)."
N.Jain, 2008 in Selected Works of Kai Lai Chung, edited by Farid AitSahlia (University of Florida, USA), Elton Hsu (Northwestern University, USA), & Ruth Williams (University of California-San Diego, USA), Chapter 1, p. 15: "This monograph deals with countable state Markov chains in both discrete time (Part I) and continuous time (Part II). [...] Much of Kai Lai's fundamental work in the field is included in this monograph. Here, for the first time, Kai Lai gave a systematic exposition of the subject which includes classification of states, ratio ergodic theorems, and limit theorems for functionals of the chain."
5. Elementary Probability Theory With Stochastic Processes. (Undergraduate Texts in Mathematics)
Description
Elementary Probability Theory with Stochastic Processes6. Elementary Probability Theory: With Stochastic Processes and an Introduction to Mathematical Finance (Undergraduate Texts in Mathematics)
Description
This book provides an introduction to probability theory and its applications. The emphasis is on essential probabilistic reasoning, which is illustrated with a large number of samples. The fourth edition adds material related to mathematical finance as well as expansions on stable laws and martingales.
From the reviews: "Almost thirty years after its first edition, this charming book continues to be an excellent text for teaching and for self study." -- STATISTICAL PAPERS
7. Markov Chains with Stationary Transition Probabilities (Grundlehren der mathematischen Wissenschaften)
Description
The theory of Markov chains, although a special case of Markov processes, is here developed for its own sake and presented on its own merits. In general, the hypothesis of a denumerable state space, which is the defining hypothesis of what we call a "chain" here, generates more clear-cut questions and demands more precise and definitive an swers. For example, the principal limit theorem ( 1. 6, II. 10), still the object of research for general Markov processes, is here in its neat final form; and the strong Markov property ( 11. 9) is here always applicable. While probability theory has advanced far enough that a degree of sophistication is needed even in the limited context of this book, it is still possible here to keep the proportion of definitions to theorems relatively low. . From the standpoint of the general theory of stochastic processes, a continuous parameter Markov chain appears to be the first essentially discontinuous process that has been studied in some detail. It is common that the sample functions of such a chain have discontinuities worse than jumps, and these baser discontinuities play a central role in the theory, of which the mystery remains to be completely unraveled. In this connection the basic concepts of separability and measurability, which are usually applied only at an early stage of the discussion to establish a certain smoothness of the sample functions, are here applied constantly as indispensable tools.8. Complex Graphs and Networks (CBMS Regional Conference Series in Mathematics)
Feature
Used Book in Good ConditionDescription
Through examples of large complex graphs in realistic networks, research in graph theory has been forging ahead into exciting new directions. Graph theory has emerged as a primary tool for detecting numerous hidden structures in various information networks, including Internet graphs, social networks, biological networks, or, more generally, any graph representing relations in massive data sets. How will we explain from first principles the universal and ubiquitous coherence in the structure of these realistic but complex networks? In order to analyze these large sparse graphs, we use combinatorial, probabilistic, and spectral methods, as well as new and improved tools to analyze these networks. The examples of these networks have led us to focus on new, general, and powerful ways to look at graph theory. The book, based on lectures given at the CBMS Workshop on the Combinatorics of Large Sparse Graphs, presents new perspectives in graph theory and helps to contribute to a sound scientific foundation for our understanding of discrete networks that permeate this information age.9. Sample Size Calculations in Clinical Research (Chapman & Hall/CRC Biostatistics Series)
Description
Praise for the Second Edition:
" this is a useful, comprehensive compendium of almost every possible sample size formula. The strong organization and carefully defined formulae will aid any researcher designing a study." -Biometrics
"This impressive book contains formulae for computing sample size in a wide range of settings. One-sample studies and two-sample comparisons for quantitative, binary, and time-to-event outcomes are covered comprehensively, with separate sample size formulae for testing equality, non-inferiority, and equivalence. Many less familiar topics are also covered " Journal of the Royal Statistical Society
Sample Size Calculations in Clinical Research, Third Edition presents statistical procedures for performing sample size calculations during various phases of clinical research and development. A comprehensive and unified presentation of statistical concepts and practical applications, this book includes a well-balanced summary of current and emerging clinical issues, regulatory requirements, and recently developed statistical methodologies for sample size calculation.
Features:
- Compares the relative merits and disadvantages of statistical methods for sample size calculations
- Explains how the formulae and procedures for sample size calculations can be used in a variety of clinical research and development stages
- Presents real-world examples from several therapeutic areas, including cardiovascular medicine, the central nervous system, anti-infective medicine, oncology, and womens health
- Provides sample size calculations for dose response studies, microarray studies, and Bayesian approaches
This new edition is updated throughout, includes many new sections, and five new chapters on emerging topics: two stage seamless adaptive designs, cluster randomized trial design, zero-inflated Poisson distribution, clinical trials with extremely low incidence rates, and clinical trial simulation.
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