View source for William Feller

{{short description|Croatian–American mathematician}}
{{Distinguish|William Fellner}}
{{Infobox scientist
| name              = William Feller
| image             =
| image_size        = 240px
| birth_name        = Vilibald Srećko Feller
| caption           = Vilim "Willy" Feller (1906-1970)
| birth_date        = {{Birth-date|July 7, 1906|}}
| birth_place       = [[Zagreb]], [[Austria-Hungary|Austro-Hungarian Monarchy]] (now [[Croatia]])
| death_date        = {{Death-date and age|January 14, 1970|July 7, 1906}}
| death_place       = New York City, US
| residence         = 
| citizenship       = 
| nationality       = Croatian–American
| fields            = [[Mathematician]]
| workplaces        = [[University of Kiel]] <br>[[University of Copenhagen]]<br> [[Stockholm University]]<br> [[University of Lund]]<br> [[Brown University]]<br>[[Cornell University]]<br>[[Princeton University]]
| alma_mater        = [[University of Zagreb]]<br>[[University of Göttingen]]
| doctoral_advisor  = [[Richard Courant]]
| academic_advisors = 
| doctoral_students = [[Patrick Billingsley]]<br>[[George Forsythe]]<br>[[Henry McKean]]<br>[[Lawrence Shepp]]<br>[[Hale Trotter]]<br>[[Benjamin Weiss]]<br>[[David A. Freedman]]<br>[[Loren Pitt]]
| notable_students  = 
| known_for         = [[Feller process]]<br>[[Feller's coin-tossing constants]]<br>[[Feller-continuous process]]<br>[[Palm calculus|Feller's paradox]]<br>[[Lindeberg's condition#Feller's theorem|Feller's theorem]]<br>[[Pareto distribution#Feller–Pareto distribution|Feller–Pareto distribution]]<br>[[Feller–Tornier constant]]<br>[[Hille-Yosida theorem|Feller–Miyadera–Phillips theorem]]<br>[[Proof by intimidation]]
| author_abbrev_bot = 
| author_abbrev_zoo = 
| awards            = [[National Medal of Science]] (USA) in Mathematical, Statistical, and Computational Sciences (1969)
| signature         = Feller_sig.jpg
| footnotes         =  
}}

'''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).<ref>Zubrinic, Darko (2006). "[http://www.croatianhistory.net/etf/feller.html#eugen William Feller (1906-1970)]". ''Croatianhistory.net''. Accessed 3 July 2018.</ref>

Eugen Feller was a famous chemist and created ''Elsa fluid'' named after his mother{{clarify|date=July 2022}}. According to [[Gian-Carlo Rota]], Eugen Feller's surname was a "Slavic tongue twister", which William changed at the age of twenty.<ref>{{cite book|last=Rota|first=Gian-Carlo|author-link=Gian-Carlo Rota|year=1996|title=''Indiscrete Thoughts''|url=https://archive.org/details/indiscretethough0000rota|url-access=registration|publisher=Birkhäuser|isbn=0-8176-3866-0}}</ref> This claim appears to be false. His forename, Vilibald, was chosen by his Catholic mother for the saint day of his birthday.<ref>{{MacTutor Biography|id=Feller|title=William Feller}}</ref>

==Career and later life==
Feller held a [[docent]] position at the University of [[Kiel]] beginning in 1928. Because he refused to sign a Nazi oath,<ref>{{cite web
 | title=Biography of William Feller
 | work=History of William Feller
 | url=http://www.croatianhistory.net/etf/feller.html#scandinavia
 | access-date=2006-06-27}}</ref> he fled the [[Nazism|Nazis]] and went to [[Copenhagen]], Denmark in 1933. He also lectured in Sweden ([[Stockholm]] and [[Lund]]).<ref>{{cite book|mr=2522825|last=Siegmund-Schultze|first=Reinhard|title=[[Mathematicians fleeing from Nazi Germany: Individual fates and global impact]]|publisher=Princeton University Press|location=Princeton, New Jersey|year=2009|pages=xxviii+471|isbn=978-0-691-14041-4}}</ref> 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.<ref>{{harv|Siegmund-Schultze|2009|p=135}}</ref>

After marrying a former student from Kiel, Clara Mary Nielsen, in 1938, he moved with her to the US in 1939. In that year he joined [[Brown University]] as an associate professor; he became a US citizen in 1944.<ref name=mt>{{mactutor|id=Feller|title=William Srecko Feller}}</ref> He moved to [[Cornell University]] in 1945 and to [[Princeton University]] in 1950. At Princeton, he became Eugene Higgins Professor of Mathematics. He remained there until his death on January 14, 1970.<ref name=nas/>

==Work==
{{more citations needed|section|date=January 2018}}
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 [[list of probabilists|probabilist]]s of the twentieth century. He 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]].<ref>Preface to his ''Mathematical Methods of Statistics''.</ref> His two-volume textbook on probability theory and its applications was called "the most successful treatise on probability ever written" by [[Gian-Carlo Rota]].<ref>Page 199: ''Indiscrete Thoughts''.</ref>  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]]s and [[differential equation]]s, where his theory of [[C0-semigroup#Infinitesimal generator|generator]]s of [[one-parameter semigroup]]s of [[stochastic process]]es gave rise to the theory of "Feller operators".

Numerous topics relating to probability are named after him, including  [[Feller process]]es, [[Feller's explosion test]], [[Feller–Brown movement]],  and the [[central limit theorem|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]]''.

==Books==
* ''An Introduction to Probability Theory and its Applications, Volume I, 3rd edition'' (1968); 1st edn. (1950);<ref>{{cite journal|author=Wolfowitz, J.|author-link=Jacob Wolfowitz|title=Review: ''An introduction to probability theory and its applications'', Vol. I, 1st ed., by W. Feller|journal=Bull. Amer. Math. Soc.|year=1951|volume=57|issue=2|pages=156–159|url=http://www.ams.org/journals/bull/1951-57-02/S0002-9904-1951-09491-4/S0002-9904-1951-09491-4.pdf|doi=10.1090/s0002-9904-1951-09491-4|doi-access=free}}</ref> 2nd edn. (1957)<ref>{{cite journal|title=Review: ''An introduction to probability theory and its applications'', Vol. I, 2nd ed., by W. Feller|journal=Bull. Amer. Math. Soc.|year=1958|volume=64|issue=6|page=393|url=http://www.ams.org/journals/bull/1958-64-06/S0002-9904-1958-10252-9/S0002-9904-1958-10252-9.pdf|doi=10.1090/s0002-9904-1958-10252-9|doi-access=free}}</ref>
* ''An Introduction to Probability Theory and its Applications, Volume II, 2nd edition'' (1971)

==Recognition==
In 1949, Feller was named a [[Fellow of the American Statistical Association]].<ref>{{cite web |title=View/Search Fellows of the ASA |url=http://www.amstat.org/awards/fellowslist.cfm |access-date=2016-07-22 |publisher=American Statistical Association |archive-date=2016-06-16 |archive-url=https://web.archive.org/web/20160616161612/https://www.amstat.org/awards/fellowslist.cfm |url-status=dead }}<!-- Not found on more recent searches; many fellows appear to have been removed from the online listing for unknown reasons --></ref> He was elected to the [[American Academy of Arts and Sciences]] in 1958, the United States [[National Academy of Sciences]] in 1960, and the [[American Philosophical Society]] in 1966.<ref>{{Cite web |title=William Feller |url=https://www.amacad.org/person/william-feller |access-date=2022-09-29 |website=American Academy of Arts & Sciences |language=en}}</ref><ref>{{Cite web |title=William Feller |url=http://www.nasonline.org/member-directory/deceased-members/20001133.html |access-date=2022-09-29 |website=www.nasonline.org}}</ref><ref>{{Cite web |title=APS Member History |url=https://search.amphilsoc.org/memhist/search?creator=William+Feller&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced |access-date=2022-09-29 |website=search.amphilsoc.org}}</ref> Feller won the [[National Medal of Science]] in 1969.<ref>{{cite web|url=https://www.nsf.gov/honorary-awards/national-medal-science/recipients/william-feller|title=William Feller|work=Recipients of the National Medal of Science|publisher=National Science Foundation|access-date=2025-04-05}}</ref> He was president of the [[Institute of Mathematical Statistics]].<ref name=nas>{{cite journal|journal=Biographical Memoirs of the National Academy of Sciences|year=2007|title=William Feller 1906–1970|first=Murray|last=Rosenblatt|url=https://www.nasonline.org/wp-content/uploads/2024/06/feller-william.pdf}}</ref>

==See also==
*[[Heston model#Basic Heston model|Feller condition]]
*[[Beta distribution]]
*[[Compound Poisson distribution]]
*[[Gillespie algorithm]]
*[[Kolmogorov equations]]
*[[Poisson point process]]
*[[Stability (probability)]]
*[[St. Petersburg paradox]]
*[[Stochastic process]]

==References==
{{Reflist}}

==External links==
{{wikiquote}}
* {{MathGenealogy|id=33019}}
* [http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/feller-william.pdf A biographical memoir] by [[Murray Rosenblatt]]
* [https://web.archive.org/web/20040615083208/http://jagor.srce.hr/zuh/velikani/vel_int.htm Croatian Giants of Science - in Croatian]
* {{MacTutor Biography|id=Feller|title=William Feller}}
* [https://web.archive.org/web/20150310024937/http://www.princeton.edu/~mudd/finding_aids/mathoral/pmcxrota.htm "Fine Hall in its golden age: Remembrances of Princeton in the early fifties" by Gian-Carlo Rota.] Contains a section on Feller at Princeton.
* [http://www.croatianhistory.net/gif/felln.jpg Feller Matriculation Form giving personal details]

{{Winners of the National Medal of Science|math-stat-comp}}

{{Authority control}}

{{DEFAULTSORT:Feller, William}}
[[Category:1906 births]]
[[Category:1970 deaths]]
[[Category:20th-century American mathematicians]]
[[Category:20th-century Croatian mathematicians]]
[[Category:Croatian mathematicians]]
[[Category:Presidents of the Institute of Mathematical Statistics]]
[[Category:Probability theorists]]
[[Category:Brown University faculty]]
[[Category:Cornell University faculty]]
[[Category:Princeton University faculty]]
[[Category:University of Göttingen alumni]]
[[Category:Faculty of Science, University of Zagreb alumni]]
[[Category:National Medal of Science laureates]]
[[Category:Croatian refugees]]
[[Category:American people of Polish-Jewish descent]]
[[Category:Croats in Austria-Hungary]]
[[Category:Croatian people of Austrian descent]]
[[Category:Croatian people of Polish-Jewish descent]]
[[Category:Scientists from Zagreb]]
[[Category:Yugoslav emigrants to the United States]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:Fellows of the American Statistical Association]]
[[Category:Members of the American Philosophical Society]]