Feller W. Selected Papers I

New York: Springer, 2015. — 836 p.This extensive selection of William Feller’s scientific papers shows the breadth of his oeuvre as well as the historical development of his scientific interests. Six seminal papers – originally written in German – on the central limit theorem, the law of large numbers, the foundations of probability theory, stochastic processes and mathematical biology are now, for the first time, available in English. The material is accompanied by detailed scholarly comments on Feller’s work and its impact, a complete bibliography, a list of his PhD students as well as a biographic sketch of his life with a sample of pictures from Feller’s family album.
William Feller was one of the leading mathematicians in the development of probability theory in the 20th century. His work continues to be highly influential, in particular in the theory of stochastic processes, limit theorems and applications of mathematics to biology. These volumes will be of value to all those interested in probability theory, analysis, mathematical biology and the history of mathematics.William Feller, 1906–1970
William Feller and Twentieth Century Probability
William Feller. A Biography
Feller’s Early Work on Measure Theory and Mathematical Foundations of Probability
Feller’s EarlyWork on Limit Theorems
Feller and Busemann on Surface Theory—Contributions to Geometry
Über algebraisch rektifizierbare transzendente Kurven
Über die Lösungen der linearen partiellen Differentialgleichungen zweiter Ordnung vom elliptischen Typus
Zur Differentiation der Lebesgueschen Integrale
Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung
On the Central Limit Theorem of Probability Theory
Krümmungseigenschaften konvexer Flächen
Zur Theorie der stochastischen Prozesse
On the Theory of Stochastic Processes (Existence and Uniqueness)
Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung. II
On the Central Limit Theorem of Probability Theory. II
Über das Gesetz der großen Zahlen
On the Law of Large Numbers
Die Grundlagen der Volterraschen Theorie des Kampfes ums Dasein in wahrscheinlichkeitstheoretischer Behandlung
The Foundations of Volterra’s Theory of the Struggle for Life in a Probabilistic Treatment
Completely Monotone Functions and Sequences
Über die Existenz von sogenannten Kollektiven
On the Existence of So-Called Kollektivs
Neuer Beweis für die Kolmogoroff-P. Lévysche Charakterisierung der unbeschränkt teilbaren Verteilungsfunktionen
On the Integro-Differential Equations of Purely Discontinuous Markoff Processes
On the Integral Equation of Renewal Theory
Some Geometric Inequalities
Generalization of a Probability Limit Theorem of Cramér
The General Form of the So-Called Law of the Iterated Logarithm
On a General Class of “Contagious” Distributions
On the Normal Approximation to the Binomial Distribution
The Fundamental Limit Theorems in Probability
Regularity Properties of a Certain Class of Surfaces
Note on the Law of Large Numbers and “Fair” Games
A Limit Theorem for Random Variables with Infinite Moments
The Law of the Iterated Logarithm for Identically Distributed Random Variables
On the Kolmogorov–Smirnov Limit Theorems for Empirical Distributions
On Probability Problems in the Theory of Counters
A Property of Power Series with Positive Coefficients
On Fluctuations in Coin-Tossing
On the Theory of Stochastic Processes, with Particular Reference to Applications
Fluctuation Theory of Recurrent Events