Collected Works I

ISBN-13: 9783642383588 / Angielski / Miękka / 2013 / 728 str.

Harald Cramer; Anders Martin-Lof

Opis

This is a collection of Harald Cramer's extensive work on number theory, probability, mathematical statistics and insurance mathematics. Many of these are not easily found in their original sources nowadays, for instance his pioneering work on risk theory published in the Skandia Insurance Company's jubilee volumes in 1930 and 1955. Despite their age, these eminent examples of Cramer's expository style remain highly readable. Cramer was one of the "fathers" of modern mathematical statistics. His famous book on the subject is still an important reference. His statistical papers included here were seminal to the subsequent development of the subject. The collection includes a complete bibliography of Cramer's work.

Spis treści

Sur une classe de series de Dirichlet.- Etudes sur la somrnation des series de Fourier.- Un theoreme sur les series de Dirichlet et son application.- Uber die Herleitung der Riemannschen Primzahlformel.- Uber die Nullstellen der Zetafunktion.- Studien tiber die Nullstellen der Riemannschen Zetafunktion.- Nombres premiers et equations indeterminees.- Bemerkung zu der vorstehenden Arbeit des Herrn E. Landau.- Some theorems concerning prime numbers.- On the distribution of primes.- Uber die Zetafunktion auf der Mittellinie des kritischen Streifens (with E. Landau).- Uber das Teilerproblem von Piltz.- Sur un probleme de M. Phragmen.- Ein Mittelwertsatz in der Primzahltheorie.- Uber zwei Satze des Herrn G. H. Hardy.- Contributions to the analytic theory of numbers.- Ein Satz tiber Dirichletsche Reihen.- Das Gesetz von Gauss und die Theorie des Risikos.- Die neuere Entwicklung der analytischen Zahlentheorie (with H. Bohr).- Remarks on correlation.- On some classes of series used in mathematical statistics.- Sur quelques points du ca1cul des probabilites.- Some notes on recent mortality investigations.- On an asymptotic expansion occurring in the theory of probability.- On the composition of elementary errors.- On the mathematical theory of risk.- The risk problem. Exordial review.- The theory of risk in its application to life insurance problems.- Su un teorema relativo alIa legge uniforme dei grandi numeri.- On the development of the mortality of the adult Swedish population since 1800 (with H. Wold).- Sugli sviluppi asintotici di funzioni di ripartizione in serie di polinomi di Hermite.- Mortality variations in Sweden: A study in graduation and forecasting (with H. Wold).- Prime numbers and probability.- Uber die Vorausberechnung der BevOlkerungsentwicklung in Schweden.- Uber eine Eigenschaft der norrnalen Verteilungsfunktion.- Some theorems on distribution functions (with H. Wold).- On the order of magnitude of the difference between consecutive prime numbers.- Sur un nouveau theoreme-limite de la theorie des probabilites.- On the representation of a function by certain Fourier integrals.- On the theory of stationary random processes.- On harmonic analysis in certain functional spaces.- A contribution to the theory of statistical estimation.- Problems in probability theory.- On the factorization of certain probability distributions.- A contribution to the theory of stochastic processes.- On some questions connected with mathematical risk.- Collective risk theory: A survey of the theory from the point of view of the theory of stochastic processes.- Ein Satz tiber geordnete Mengen von Wahrscheinlichkeitsverteilungen.- On the linear prediction problem for certain stochastic processes.- On some classes of nonstationary stochastic processes.- On the structure of purely non-deterministic stochastic processes.- Model building with the aid of stochastic processes.- On the maximum of a normal stationary stochastic process.- Decompositions orthogonales de certains processus stochastiques.- On the approximation to a stable probability distribution.- On asymptotic expansions for sums of independent random variables with a limiting stable distribution.- Stochastic processes as curves in Hilbert space.- The moments of the number of crossings of a level by a stationary normal process (with M. R. Leadbetter).- A limit theorem for the maximum values of certain stochastic processes.- On the intersections between the trajectories of a normal stationary stochastic process and a high level.- On stochastic processes whose trajectories have no discontinuities of the second kind.- On extreme values of certain stochastic processes.- A contribution to the multiplicity theory of stochastic processes.- Historical review of Filip Lundberg's works on risk theory.- On streams of random events.-Structural and statistical problems for a class of stochastic processes.- On distribution function-moment relationships in a stationary point process (with M. R. Leadbetter and R. J. Serfling).- On the history of certain expansions used in mathematical statistics.- On the multiplicity of a stochastic vector process.- Half a century with probability theory. Some personal recollections.- On the multiplicity of a stochastic vector process.- On some points of the theory of stochastic processes.- Mathematical probability and statistical inference.- Bibliography.- Acknowledgements.