# William Feller

William Feller | |
---|---|

Born | Vilibald Srećko Feller July 7, 1906 |

Died | January 14, 1970 | (aged 63)

Nationality | Croatian–American |

Alma mater | University of Zagreb University of Göttingen |

Known for | Feller process Feller's coin-tossing constants Feller-continuous process Feller's paradox Feller's theorem Feller–Pareto distribution Feller–Tornier constant Feller–Miyadera–Phillips theorem Proof by intimidation Stars and bars |

Awards | National Medal of Science (USA) in Mathematical, Statistical, and Computational Sciences (1969) |

Scientific career | |

Fields | Mathematician |

Institutions | University of Kiel University of Copenhagen University of Stockholm University of Lund Brown University Cornell University Princeton University |

Doctoral advisor | Richard Courant |

Doctoral students | Patrick Billingsley George Forsythe Robert Kurtz Henry McKean Lawrence Shepp Hale Trotter Benjamin Weiss David A. Freedman |

Influences | Stanko Vlögel |

Signature | |

**William "Vilim" Feller** (July 7, 1906 – January 14, 1970), born **Vilibald Srećko Feller**, was a Croatian-American mathematician specializing in probability theory.

## Early life and education

Feller was born in Zagreb to Ida Oemichen-Perc, a Croatian-Austrian Catholic, and Eugen Viktor Feller, son of a Polish-Jewish father (David Feller) and an Austrian 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 position at the University of Kiel beginning in 1928. Because he refused to sign a Nazi oath, he fled the Nazis and went to Copenhagen, Denmark in 1933. He also lectured in Sweden (Stockholm and Lund). 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. where he became a citizen in 1944 and was on the faculty at Brown and Cornell. In 1950 he became a professor at Princeton University.

The works of Feller are contained in 104 papers and two books on a variety of topics such as mathematical analysis, theory of measurement, functional analysis, geometry, and differential equations 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 probability theory as a branch of mathematical analysis 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. 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 chains and differential equations, where his theory of generators of one-parameter semigroups of stochastic processes gave rise to the theory of "Feller operators".

## Results

Numerous topics relating to probability are named after him, including Feller processes, Feller's explosion test, Feller–Brown movement, and the Lindeberg–Feller theorem. Feller made fundamental contributions to renewal theory, Tauberian theorems, random walks, diffusion processes, and the law of the iterated logarithm. Feller was among those early editors who launched the journal *Mathematical Reviews*.

## 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 won the National Medal of Science in 1969.^{[citation needed]}
He was president of the Institute of Mathematical Statistics.^{[citation needed]}

In 1949, he was named a Fellow of the American Statistical Association. He was elected to the National Academy of Sciences in 1980.

## See also

- 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