Selected Papers II

ISBN-13: 9783319168555 / Angielski / Twarda / 2015 / 785 str.

William Feller; Rene L. Schilling; Zoran Vondracek

Opis

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. Volume I covers the early years 1928-1949, featuring the celebrated Lindeberg-Feller Central Limit Theorem, while Volume II contains papers from 1950-1971 when the theory of Feller processes and boundaries had been developed. 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.

Recenzje

"Selected Papers II includes papers published from 1951 to 1970 on the semigroup treatment of Markov processes, regular variation, further work on limit and renewal theory, and other topics ... . There is a great deal on offer in these two excellent volumes, and they deserve a place in any library collection devoted to probability!" (Anthony G. Pakes, Mathematical Reviews, February, 2017)

Spis treści

Preface. - Curriculum Vitae: William Feller 1906–1970.- Bibliography of William Feller. - PhD Students of William Feller. - R. L. Schilling and W. A. Woyczy´ nski: William Feller. A Biography. - E. Baake and A. Wakolbinger: Feller’s Contributions to Mathematical Biology.- N. Jacob: Feller on Differential Operators and Semi-groups. - M. Fukushima: Feller’s Contributions to the One-Dimensional Diffusion Theory and Beyond.- G. Peskir: On Boundary Behaviour of One-Dimensional Diffusions: From Brown to Feller and Beyond. - R. Maller: Feller’s Work in Renewal Theory, the Law of the Iterated Logarithm and Karamata Theory. – Selected Papers of William Feller.

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O autorze

William Feller (1906 - 1970) was one of the most distinguished figures in probability theory of the 20th century. His work contains seminal contributions to the areas of Stochastic Processes (in particular: “Feller” processes, boundary theory, analytic treatment of stochastic processes), Limit theorems for random variables (Central Limit Theorem, Fluctuation Theory) and Applications of Stochastic Processes to Mathematical Biology. Feller was a prolific writer and even his “minor” contributions are still quoted nowadays, e.g. Contributions to measure theory (differentiation of measures), Contributions to geometry (Feller-Alexandrov-Busemann curvature). Among his almost twenty doctoral students one finds some of the most distinguished mathematicians, including Patrick Billingsley, Henry McKean, Hale Trotter, Frank Knight, David Freedman, Martin Silverstein, Lawrence Shepp.