Probability, Statistics, and Mathematics: Papers in Honor of Samuel Karlin is a collection of papers dealing with probability, statistics, and mathematics. Conceived in honor of Polish-born mathematician Samuel Karlin, the book covers a wide array of topics, from the second-order moments of a stationary Markov chain to the exponentiality of the local time at hitting times for reflecting diffusions. Smoothed limit theorems for equilibrium processes are also discussed. Comprised of 24 chapters, this book begins with an introduction to the second-order moments of a stationary Markov chain, paying particular attention to the consequences of the autoregressive structure of the vector-valued process and how to estimate the stationary probabilities from a finite sequence of observations. Subsequent chapters focus on A. Selberg's second beta integral and an integral of mehta; a normal approximation for the number of local maxima of a random function on a graph; nonnegative polynomials on polyhedra; and the fundamental period of the queue with Markov-modulated arrivals. The rate of escape problem for a class of random walks is also considered. This monograph is intended for students and practitioners in the fields of statistics, mathematics, and economics.

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Information

Publisher

Academic Press

Year

2014

ISBN

9781483216003

Topic

Mathematics

Subtopic

Applied Mathematics

Index

Mathematics

Front Cover
Probability, Statistics, and Mathematics: Papers in Honor of Samuel Karlin
Copyright Page
Table of Contents
LIST OF CONTRIBUTORS
FOREWORD
PUBLICATIONS OF SAMUEL KARLIN
Chapter 1. Second-Order Moments of a Stationary Markov Chain and Some Applications
Chapter 2. A "Dynamic" Proof of the Frobenius-Perron Theorem for Metzler Matrices
Chapter 3. Selberg's Second Beta Integral and an Integral of Mehta
Chapter 4. Exponentiality of the Local Time at Hitting Times for Reflecting Diffusions and an Application
Chapter 5. A Normal Approximation for the Number of Local Maxima of a Random Function on a Graph
Chapter 6. Operator Solution of Infinite Gδ Games of Imperfect Information
Chapter 7. Smoothed Limit Theorems for Equilibrium Processes
Chapter 8. Supercritical Branching Processes with Countably Many Types and the Size of Random Cantor Sets
Chapter 9. Maxima of Random Quadratic Forms on a Simplex
Chapter 10. Total Positivity and Renewal Theory
Chapter 11. Some Remarks on Nonnegative Polynomials on Polyhedra
Chapter 12. The Fundamental Period of the Queue with Markov-Modulated Arrivals
Chapter 13. Some Remarks on a Limiting Diffusion for Decomposable Branching Processes
Chapter 14. Some Results on Repeated Risktaking
Chapter 15. The Rate of Escape Problem for a Class of Random Walks
Chapter 16. Recent Advances on the Integrated Cauchy Functional Equation and Related Results in Applied Probability
Chapter 17. A Note on Maximum Entropy
Chapter 18. The Various Linear Fractional Lévy Motions
Chapter 19. Bonferroni-Type Probability Bounds as an Application of the Theory of Tchebycheff Systems
Chapter 20. The √N Law and Repeated Risktaking
Chapter 21. A Theorem in Search of a Simple Proof
Chapter 22. Grade of Membership Representations: Concepts and Problems
Chapter 23. Uniform Error Bounds Involving Logspline Models
Chapter 24. An Alternative to Cp Model Selection that Emphasizes the Quality of Coefficient Estimation