William "Vilim" Feller (July 7, 1906 – January 14, 1970), born Vilibald Srećko Feller, was a

Croatia , image_flag = Flag of Croatia.svg , image_coat = Coat of arms of Croatia.svg , anthem = "Lijepa naša domovino"("Our Beautiful Homeland") , image_map = , map_caption = , capit ...

American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, pe ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

specializing in

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

Early life and education

Feller was born in

Zagreb Zagreb ( , , , ) is the capital (political), capital and List of cities and towns in Croatia#List of cities and towns, largest city of Croatia. It is in the Northern Croatia, northwest of the country, along the Sava river, at the southern slop ...

to Ida Oemichen-Perc, a Croatian-

Austrian Austrian may refer to: * Austrians, someone from Austria or of Austrian descent ** Someone who is considered an Austrian citizen, see Austrian nationality law * Austrian German dialect * Something associated with the country Austria, for example: ...

Catholic The Catholic Church, also known as the Roman Catholic Church, is the largest Christian church, with 1.3 billion baptized Catholics worldwide . It is among the world's oldest and largest international institutions, and has played a ...

, and Eugen Viktor Feller, son of a

Polish-Jewish The history of the Jews in Poland dates back at least 1,000 years. For centuries, Poland was home to the largest and most significant Ashkenazi Jewish community in the world. Poland was a principal center of Jewish culture, because of the lon ...

father (David Feller) and an

mother (Elsa Holzer). Eugen Feller was a famous chemist and created ''Elsa fluid'' named after his mother. According to Gian-Carlo Rota, Eugen Feller's surname was a "Slavic tongue twister", which William changed at the age of twenty. This claim appears to be false. His forename, Vilibald, was chosen by his Catholic mother for the saint day of his birthday.

Work

Feller held a

docent The title of docent is conferred by some European universities to denote a specific academic appointment within a set structure of academic ranks at or below the full professor rank, similar to a British readership, a French " ''maître de conf ...

position at the University of

Kiel Kiel () is the capital and most populous city in the northern Germany, German state of Schleswig-Holstein, with a population of 246,243 (2021). Kiel lies approximately north of Hamburg. Due to its geographic location in the southeast of the J ...

beginning in 1928. Because he refused to sign a Nazi oath, he fled the

Nazis Nazism ( ; german: Nazismus), the common name in English for National Socialism (german: Nationalsozialismus, ), is the far-right totalitarian political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Na ...

and went to

Copenhagen Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan ar ...

, Denmark in 1933. He also lectured in Sweden (

Stockholm Stockholm () is the Capital city, capital and List of urban areas in Sweden by population, largest city of Sweden as well as the List of urban areas in the Nordic countries, largest urban area in Scandinavia. Approximately 980,000 people liv ...

and

Lund Lund (, , ) is a city in the southern Swedish provinces of Sweden, province of Scania, across the Øresund, Öresund strait from Copenhagen. The town had 91,940 inhabitants out of a municipal total of 121,510 . It is the seat of Lund Municipali ...

). As a refugee in Sweden, Feller reported being troubled by increasing fascism at the universities. He reported that the mathematician Torsten Carleman would offer his opinion that Jews and foreigners should be executed. Finally, in 1939 he arrived in the

U.S. The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country Continental United States, primarily located in North America. It consists of 50 U.S. state, states, a Washington, D.C., ...

where he became a

citizen Citizenship is a "relationship between an individual and a state to which the individual owes allegiance and in turn is entitled to its protection". Each state determines the conditions under which it will recognize persons as its citizens, and ...

in 1944 and was on the faculty at

Brown Brown is a color. It can be considered a composite color, but it is mainly a darker shade of orange. In the CMYK color model used in printing or painting, brown is usually made by combining the colors orange and black. In the RGB color model used ...

and

Cornell Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach an ...

. In 1950 he became a professor at

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

. The works of Feller are contained in 104 papers and two books on a variety of topics such as

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

, theory of

measurement Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared ...

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, and

differential equations In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

in addition to his work in mathematical statistics and probability. Feller was one of the greatest probabilists of the twentieth century, who is remembered for his championing of

as a branch of

in Sweden and the United States. In the middle of the 20th century, probability theory was popular in France and Russia, while mathematical statistics was more popular in the United Kingdom and the United States, according to the Swedish statistician,

Harald Cramér Harald Cramér (; 25 September 1893 – 5 October 1985) was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory. John Kingman described him as "one of the giants of statist ...

. His two-volume textbook on probability theory and its applications was called "the most successful treatise on probability ever written" by Gian-Carlo Rota. By stimulating his colleagues and students in Sweden and then in the United States, Feller helped establish research groups studying the analytic theory of probability. In his research, Feller contributed to the study of the relationship between

Markov chain A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happe ...

s and

differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

s, where his theory of

generator Generator may refer to: * Signal generator, electronic devices that generate repeating or non-repeating electronic signals * Electric generator, a device that converts mechanical energy to electrical energy. * Generator (circuit theory), an eleme ...

s of

one-parameter semigroup In mathematics, a ''C''0-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function. Just as exponential functions provide solutions of scalar linear constant coefficient ordinary differ ...

s of

stochastic process In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ...

es gave rise to the theory of "Feller operators".

Results

Numerous topics relating to probability are named after him, including

Feller process In probability theory relating to stochastic processes, a Feller process is a particular kind of Markov process. Definitions Let ''X'' be a locally compact Hausdorff space with a countable base. Let ''C''0(''X'') denote the space of all rea ...

es, Feller's explosion test, Feller–Brown movement, and the Lindeberg–Feller theorem. Feller made fundamental contributions to

renewal theory Renewal theory is the branch of probability theory that generalizes the Poisson process for arbitrary holding times. Instead of exponentially distributed holding times, a renewal process may have any independent and identically distributed (IID) ho ...

, Tauberian theorems,

random walks In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb Z ...

diffusion processes Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of ...

, and the

law of the iterated logarithm In probability theory, the law of the iterated logarithm describes the magnitude of the fluctuations of a random walk. The original statement of the law of the iterated logarithm is due to A. Ya. Khinchin (1924). Another statement was given by A ...

. Feller was among those early editors who launched the journal ''

Mathematical Reviews ''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also pu ...

''.

Notable books

* ''An Introduction to Probability Theory and its Applications, Volume I, 3rd edition'' (1968); 1st edn. (1950); 2nd edn. (1957) * ''An Introduction to Probability Theory and its Applications, Volume II, 2nd edition'' (1971)

Recognition

Feller was elected to the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...

in 1958, the United States

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...

in 1960, and the

American Philosophical Society The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and communit ...

in 1966. Feller won the National Medal of Science in 1969. He was president of the

Institute of Mathematical Statistics The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts o ...

. In 1949, he was named a

Fellow of the American Statistical Association Like many other academic professional societies, the American Statistical Association (ASA) uses the title of Fellow of the American Statistical Association as its highest honorary grade of membership. The number of new fellows per year is limited ...

. He was elected to the

in 1980.

References

External links

*
A biographical memoir
by

Murray Rosenblatt Murray Rosenblatt (September 7, 1926 – October 9, 2019) was a statistician specializing in time series analysis who was a professor of mathematics at the University of California, San Diego. He received his Ph.D. at Cornell University. He was als ...

Croatian Giants of Science - in Croatian
*

Contains a section on Feller at Princeton.
Feller Matriculation Form giving personal details
{{DEFAULTSORT:Feller, William 1906 births 1970 deaths 20th-century American mathematicians 20th-century Croatian people Croatian mathematicians Presidents of the Institute of Mathematical Statistics Probability theorists Brown University faculty Cornell University faculty Princeton University faculty University of Göttingen alumni Faculty of Science, University of Zagreb alumni National Medal of Science laureates Croatian refugees American people of Polish-Jewish descent Croatian Austro-Hungarians Croatian people of Austrian descent Croatian people of Polish-Jewish descent Scientists from Zagreb Yugoslav emigrants to the United States Members of the United States National Academy of Sciences Fellows of the American Statistical Association Members of the American Philosophical Society