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.

List of ContributorsForewordPublications of Samuel KarlinPh.D. Students of Samuel KarlinSecond-Order Moments of a Stationary Markov Chain and Some ApplicationsA "Dynamic" Proof of the Frobenius-Perron Theorem for Metzler MatricesSelberg's Second Beta Integral and an Integral of MehtaExponentiality of the Local Time at Hitting Times for Reflecting Diffusions and an ApplicationA Normal Approximation for the Number of Local Maxima of a Random Function on a GraphOperator Solution of Infinite Gd Games of Imperfect InformationSmoothed Limit Theorems for Equilibrium ProcessesSupercritical Branching Processes with Countably Many Types and the Size of Random Cantor SetsMaxima of Random Quadratic Forms on a SimplexTotal Positivity and Renewal TheorySome Remarks on Nonnegative Polynomials on PolyhedraThe Fundamental Period of the Queue with Markov-Modulated ArrivalsSome Remarks on a Limiting Diffusion for Decomposable Branching ProcessesSome Results on Repeated RisktakingThe Rate of Escape Problem for a Class of Random WalksRecent Advances on the Integrated Cauchy Functional Equation and Related Results in Applied ProbabilityA Note on Maximum EntropyThe Various Linear Fractional Levy MotionsBonferroni-Type Probability Bounds as an Application of the Theory of Tchebycheff SystemsThe vN Law and Repeated RisktakingA Theorem in Search of a Simple ProofGrade of Membership Representations: Concepts and ProblemsUniform Error Bounds Involving Logspline ModelsAn Alternative to Cp Model Selection that Emphasizes the Quality of Coefficient Estimation