Probability, Statistics, and Mathematics

Probability, Statistics, and Mathematics

Papers in Honor of Samuel Karlin

1st Edition - October 28, 1989

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  • Editors: T. W. Anderson, Krishna B. Athreya, Donald L. Iglehart
  • eBook ISBN: 9781483216003

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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

Product details

  • No. of pages: 412
  • Language: English
  • Copyright: © Academic Press 1989
  • Published: October 28, 1989
  • Imprint: Academic Press
  • eBook ISBN: 9781483216003

About the Editors

T. W. Anderson

Krishna B. Athreya

Donald L. Iglehart

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