Contributions to Probability : A Collection of Papers Dedicated to Eugene Lukacs

Contributions to Probability: A Collection of Papers Dedicated to Eugene Lukacs is a collection of papers that reflect Professor Eugene Lukacs'broad range of research interests. This text celebrates the 75th birthday of Eugene Lukacs, mathematician, teacher, and research worker in probability and mathematical statistics. This book is organized into two parts encompassing 23 chapters. Part I consists of papers in probability theory, limit theorems, and stochastic processes. This part also deals with the continuation and arithmetic of distribution functions, the arc sine law, Fourier transform methods, and nondifferentiality of the Wiener sheet. Part II includes papers in information and statistical theories. This book will prove useful to statisticians, mathematicians, and advance mathematics students. Content: Inside Front Cover, Page ii Front Matter, Page iii Copyright, Page iv List of Contributors, Pages xiii-xv Preface, Pages xvii-xviii Eugene Lukacs, Pages xix-xxi Lagrange's Theorem and Thin Subsequences of Squares, Pages 3-9, Paul Erdös, Melvyn B. Nathanson A Kind of Random (= Stochastic) Integral, Pages 11-28, D.A. Kappos Continuation of Distribution Functions, Pages 29-48, H.-J. Rossberg, B. Jesiak, G. Siegel The Arc Sine Law of Paul Lévy, Pages 49-63, Lajos Takács General Limit Theorems for Products with Applications to Convolution Products of Measures, Pages 65-76, Harald Bergström Stable Limit Law and Weak Law of Large Numbers for Hilbert Space with “Large-” Rates, Pages 77-100, P.L. Butzer, L. Hahn, M.Th. Roeckerath The Arithmetic of Distribution Functions, Pages 101-114, Roger Cuppens On the Tails of a Class of Infinitely Divisible Distributions, Pages 115-122, Carl-Gustav Esseen Fourier Transform Methods in the Study of Limit Theorems in a Hilbert Space, Pages 123-137, R.G. Laha, V.K. Rohatgi Polynomials in Gaussian Variables and Infinite Divisibility?, Pages 139-142, M. Rosenblatt On the Nondifferentiability of the Wiener Sheet, Pages 143-150, M. Csörgő, P. Révész The Degree of Vertices on a Randomly Growing Tree, Pages 151-156, J. Gani, R. Morton Uniform Convergence of Random Trigonometric Series and Sample Continuity of Weakly Stationary Processes, Pages 157-171, Tatsuo Kawata Stochastic Equations Driven by Random Measures and Semimartingales, Pages 173-188, Michel Metivier Derivations and Information Functions: (A Tale of Two Surprises and a Half), Pages 191-200, J. Aczél Entropy of the Sum of Independent Bernoulli Random Variables and of the Multinomial Distribution, Pages 201-206, L.A. Shepp, I. Olkin On the Concept and Measure of Information Contained in an Observation, Pages 207-214, István Vincze The Empirical Characteristic Process When Parameters Are Estimated, Pages 215-230, Sándor Csörgő Identifiability, Pages 231-246, M. Deistler, G. Tintner On a Multivariate Extension of the Behrens–Fisher Law, Pages 247-253, Daniel Dugué Constant Regression of Quadratic Statistics on the Sum of Random Variables Defined on a Markov Chain, Pages 255-266, B. Gyires Invariance Principles for Rank Statistics for Testing Independence, Pages 267-282, Madan L. Puri, Lanh T. Tran Integral Transformations of Distributions and Estimates of Parameters of Multidimensional Spherically Symmetric Stable Laws, Pages 283-305, V.M. Zolotarev Eugene Lukacs: Bibliography, Pages 307-311