Probability, Statistics, and Mathematics - 1st Edition - ISBN: 9780120584703, 9781483216003

Probability, Statistics, and Mathematics

1st Edition

Papers in Honor of Samuel Karlin

Editors: T. W. Anderson Krishna B. Athreya Donald L. Iglehart
eBook ISBN: 9781483216003
Imprint: Academic Press
Published Date: 28th October 1989
Page Count: 412
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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.

Table of Contents

List of Contributors


Publications of Samuel Karlin

Ph.D. Students of Samuel Karlin

Second-Order Moments of a Stationary Markov Chain and Some Applications

A "Dynamic" Proof of the Frobenius-Perron Theorem for Metzler Matrices

Selberg's Second Beta Integral and an Integral of Mehta

Exponentiality of the Local Time at Hitting Times for Reflecting Diffusions and an Application

A Normal Approximation for the Number of Local Maxima of a Random Function on a Graph

Operator Solution of Infinite Gδ Games of Imperfect Information

Smoothed Limit Theorems for Equilibrium Processes

Supercritical Branching Processes with Countably Many Types and the Size of Random Cantor Sets

Maxima of Random Quadratic Forms on a Simplex

Total Positivity and Renewal Theory

Some Remarks on Nonnegative Polynomials on Polyhedra

The Fundamental Period of the Queue with Markov-Modulated Arrivals

Some Remarks on a Limiting Diffusion for Decomposable Branching Processes

Some Results on Repeated Risktaking

The Rate of Escape Problem for a Class of Random Walks

Recent Advances on the Integrated Cauchy Functional Equation and Related Results in Applied Probability

A Note on Maximum Entropy

The Various Linear Fractional Levy Motions

Bonferroni-Type Probability Bounds as an Application of the Theory of Tchebycheff Systems

The √N Law and Repeated Risktaking

A Theorem in Search of a Simple Proof

Grade of Membership Representations: Concepts and Problems

Uniform Error Bounds Involving Logspline Models

An Alternative to Cp Model Selection that Emphasizes the Quality of Coefficient Estimation


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© Academic Press 1989
Academic Press
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About the Editor

T. W. Anderson

Krishna B. Athreya

Donald L. Iglehart

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