David Williams (mathematician)

David Williams
Williams in 1975
Born
Gower Peninsula, Swansea, UK
Alma materJesus College, Oxford
Known forPath decomposition of Brownian excursions
Scientific career
InstitutionsStanford University
University of Durham
University of Cambridge
University College of Swansea
University of Bath
ThesisRandom time substitution in Markov chains (1962)
Doctoral advisorD. G. Kendall and G. E. H. Reuter
Doctoral studentsMartin Baxter
Chris Rogers

David Williams FRS is a Welsh mathematician who works in probability theory.

Early life and education

David Williams was born at Gorseinon, near Swansea, Wales. He was educated at Gowerton Grammar School, winning a mathematics scholarship to Jesus College, Oxford, and went on to obtain a DPhil under the supervision of David George Kendall and Gerd Edzard Harry Reuter, with a thesis titled Random time substitution in Markov chains.[1]

Career

Williams held posts at the Stanford University (1962–63), University of Durham, University of Cambridge (1966–69), and at Swansea University (1969–85), where he was promoted to a personal chair in 1972.

In 1985, he was elected to the Professorship of Mathematical Statistics, University of Cambridge, where he remained until 1992, serving as Director of the Statistical Laboratory between 1987 and 1991.[2] Following this, he held the Chair of Mathematical Sciences jointly with the Mathematics and Statistics Groups at the University of Bath.

In 1999, he returned to Swansea University, where he currently holds a Research Professorship.

Williams's research interests encompass Brownian motion, diffusions, Markov processes, martingales and Wiener–Hopf theory. Recognition for his work includes being elected Fellow of the Royal Society in 1984, where he was cited for his achievements on the construction problem for Markov chains and on path decompositions for Brownian motion,[3] and being awarded the London Mathematical Society's Pólya Prize in 1994.[4]

One of his main discoveries is the decomposition of Brownian paths with respect to their maximum.[5]

He is the author of Probability With Martingales and Weighing the Odds, and co-author (with L. C. G. Rogers) of both volumes of Diffusions, Markov Processes and Martingales.

Books

  • Diffusions, Markov processes, and martingales, Wiley 1979; 2nd. edn. with L. C. G. Rogers: Diffusions, Markov processes, and martingales, Volume One: Foundations, Wiley 1995;[6] reprinting of 2nd edn. Cambridge University Press 2000
  • with L. C. G. Rogers: Diffusions, Markov processes, and martingales, Volume Two: Itō calculus, Wiley 1988; 2nd edn. Cambridge University Press 2000
  • Probability with martingales, Cambridge Mathematical Textbooks, Cambridge University Press 1991
  • Weighing the Odds: a course in probability and statistics, Cambridge University Press 2001
  • ed. with J. C. R. Hunt, O. M. Phillips: Turbulence and stochastic processes. Kolmogorov´s ideas 50 years on, London, Royal Society 1991

References

  1. ^ Index to Theses
  2. ^ Whittle, Peter (2001) [1993]. "1985–92 Martingales and the Mabinogion". A Realised Path: The Cambridge Statistical Laboratory up to 1993. University of Cambridge. Archived from the original on 19 December 2013. Retrieved 24 January 2008.
  3. ^ "Williams, David". Library and Archive catalogue. The Royal Society. Archived from the original on 12 March 2020. Retrieved 24 January 2008.
  4. ^ "LMS Prizewinners". London Mathematical Society. Archived from the original on 17 December 2005. Retrieved 24 January 2008.
  5. ^ Williams, David (1970). "Decomposing the Brownian path". Bull. Amer. Math. Soc. 76 (4): 871–873. doi:10.1090/S0002-9904-1970-12591-5. Retrieved 12 October 2020.
  6. ^ Falkner, Neil (1997). "Review: Diffusions, Markov processes, and martingales, Volume One: Foundations, by L. C. G. Rogers and D. Williams". Bull. Amer. Math. Soc. (N.S.). 34 (1): 57–62. doi:10.1090/s0273-0979-97-00693-9.

Read other articles:

Michelle Obama

Michelle Obama Ibu Negara Amerika SerikatMasa jabatan20 Januari 2009 – 20 Januari 2017PresidenBarack Obama PendahuluLaura BushPenggantiMelania Trump Informasi pribadiLahirMichelle LaVaughn Robinson17 Januari 1964 (umur 60)Chicago, IllinoisKebangsaanAmerika SerikatPartai politikDemokratSuami/istriBarack Obama (1992-sekarang)AnakMalia Obama Sasha ObamaTempat tinggalChicago, ILAlma materPrinceton University, (A.B.)Harvard Law School, (J.D.)ProfesiPengacaraTanda tanganSunting kota...

 

Fanjingshan

Artikel ini sebatang kara, artinya tidak ada artikel lain yang memiliki pranala balik ke halaman ini.Bantulah menambah pranala ke artikel ini dari artikel yang berhubungan atau coba peralatan pencari pranala.Tag ini diberikan pada Oktober 2022. FanjingshanBatu CendawanTitik tertinggiKetinggian2.570,0 m (8.431,8 ft)PenamaanNama terjemahanGunung Tanah Murni Brahma (bahasa Tionghoa)GeografiFanjingshanTongren, Guizhou, Tiongkok Situs Warisan Dunia UNESCONama resmiFanjingshanJenisAla...

 

Abyei

Abyeiأبيي BenderaStatusPengakuan terbatasIbu kotaKota AbyeiKelompok etnik Abyeinese, Upeso, BathunsafkeDemonimAxnaxazunPendirian• Comprehensive Peace Agreement 9 Januari 2005• Pendirian Pemerintahan Daerah Abyei 31 Agustus 2008• Didirikan 2009 Luas - Total10.546 km2Populasi - Perkiraan 2014124.390 - Total200,751GiniOS$Error: Invalid Gini valueMata uangPound AbyeiZona waktuWaktu Abyei (UTC-20.05)Kode telepon+4025,+2583,+330 Sunti...

Judah P. Benjamin

Judah P. Benjamin Masa jabatan18 Maret 1862 – 10 Mei 1865PresidenJefferson Davis PendahuluWilliam BrownePenggantiPetahanaMasa jabatan17 September 1861 – 24 Maret 1862PresidenJefferson Davis PendahuluLeRoy WalkerPenggantiGeorge RandolphMasa jabatan25 Februari 1861 – 15 November 1861PresidenJefferson Davis PenggantiWade KeyesSenator Amerika Serikat dari LouisianaMasa jabatan4 Maret 1853 – 4 Februari 1861 PendahuluSolomon DownsPenggantiJohn Harris (186...

 

Serie B 1999-2000

Disambiguazione – Se stai cercando altri significati, vedi Serie B 1999-2000 (disambigua). Serie B 1999-2000Serie B TIM 1999-2000 Competizione Serie B Sport Calcio Edizione 68ª Organizzatore Lega Calcio Date dal 29 agosto 1999al 18 giugno 2000 Luogo  Italia Partecipanti 20 Formula girone unico Risultati Vincitore Vicenza(3º titolo) Altre promozioni AtalantaBresciaNapoli Retrocessioni CesenaAlzano VirescitSavoiaFermana Statistiche Miglior marcatore Cosimo Francioso (24) ...

 

2015–16 Hofstra Pride women's basketball team

Intercollegiate basketball season 2015–16 Hofstra Pride women's basketballWNIT, QuarterfinalsConferenceColonial Athletic AssociationRecord25–9 (13–5 CAA)Head coachKrista Kilburn-Steveskey (10th season)Assistant coaches Faisal Khan Denise King Michael Gibson Home arenaHofstra ArenaSeasons← 2014–152016–17 → 2015–16 CAA women's basketball standings vte Conf Overall Team W   L   PCT W   L   PCT James Madison † 17 – 1   ....

Yusril Ihza Mahendra

Yusril Ihza MahendraYusril Ihza Mahendra Menteri Sekretaris Negara Indonesia ke-14Masa jabatan21 Oktober 2004 – 9 Mei 2007PresidenSusilo Bambang Yudhoyono PendahuluBambang KesowoPenggantiHatta RajasaMenteri Hukum dan Hak Asasi Manusia Indonesia ke-22Masa jabatan10 Agustus 2001 – 20 Oktober 2004PresidenMegawati Soekarnoputri PendahuluMohammad MahfudPenggantiHamid AwaluddinMenteri Hukum dan Perundang-undangan Indonesia ke-22Masa jabatan29 Oktober 1999 –&...

 

Salvia judaica

Salvia judaica Klasifikasi ilmiah Kerajaan: Plantae (tanpa takson): Angiospermae (tanpa takson): Eudicots Ordo: Lamiales Famili: Lamiaceae Genus: Salvia Spesies: Salvia judaica Nama binomial Salvia judaicaBoiss. Salvia judaica adalah spesies tumbuhan yang tergolong ke dalam famili Lamiaceae. Spesies ini juga merupakan bagian dari ordo Lamiales. Spesies Salvia judaica sendiri merupakan bagian dari genus Salvia.[1] Nama ilmiah dari spesies ini pertama kali diterbitkan oleh Boiss.. Refe...

 

José Aparecido dos Santos

Questa voce sull'argomento cestisti brasiliani è solo un abbozzo. Contribuisci a migliorarla secondo le convenzioni di Wikipedia. Segui i suggerimenti del progetto di riferimento. Joy Nazionalità  Brasile Altezza 201 cm Peso 88 kg Pallacanestro Ruolo Centro Carriera Squadre di club  Corinthians Paulista Nazionale 1968-1973 Brasile Palmarès  Mondiali Argento Jugoslavia 1970  Campionati sudamericani Oro Paraguay 1968 Argento Uruguay 1969 Oro Uruguay 1971 Oro Colombi...

Gangubai Hangal

Gangubai Hangalಗಂಗೂಬಾಯಿ ಹಾನಗಲ್Gangubai dengan putrinya Krishna pada 1930anInformasi latar belakangLahir(1913-03-05)5 Maret 1913[1][2]Hangal, Karnataka, India[3]AsalDharwad, Karnataka, India[1][2]Meninggal21 Juli 2009(2009-07-21) (umur 96)Hubli, Karnataka, India[2]GenreMusik klasik HindustaniPekerjaanPenyanyiTahun aktif1931–2006[4] Gangubai Hangal (5 Maret 1913 – 21 Juli 2009) adalah seor...

 

Dead Man Incorporated

Predominantly white prison and street gang founded in Maryland, US This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Dead Man Incorporated – news · newspapers · books · scholar · JSTOR (February 2022) (Learn how and when to remove this message) Dead Man IncorporatedDead Man Incorporated gang tattooFounded2000&...

 

Damoh district

This article is about the district. For its eponymous headquarters, see Damoh. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Damoh district – news · newspapers · books · scholar · JSTOR (September 2011) (Learn how and when to remove this message) District of Madhya Pradesh in IndiaDamoh districtDistrict of...

Shadow Minister for Employment

Shadow Minister for EmploymentIncumbentAlison McGovernsince 4 December 2021AppointerLeader of the OppositionInaugural holderBarbara CastleFormation19 June 1970WebsiteThe Shadow Cabinet The office of Shadow Minister for Employment is a position on the United Kingdom's Official Opposition frontbench, and has occasionally been a position in the Shadow Cabinet. From 1970 to 1995, the duty of the office holder was to scrutinise the actions of the government's Secretary of State for Employmen...

 

Yunieska Robles

Questa voce o sezione sull'argomento pallavolisti non è ancora formattata secondo gli standard. Contribuisci a migliorarla secondo le convenzioni di Wikipedia. Segui i suggerimenti del progetto di riferimento. Yunieska RoblesNazionalità Cuba Altezza185 cm Peso70 kg Pallavolo RuoloSchiacciatrice/Opposto Squadra Šygys Öskemen CarrieraSquadre di club ?-2012 Isla de la Juventud2012-2013 Lokomotiv Biləcəri2013-2014 Azərreyl2015 Al-Ahly2015- Šygys Ö...

 

Гран-при Канады 1974 года

Гран-при Канады 1974 годаангл. XIVth Canadian Grand Prix Дата 22 сентября 1974 года Место Канада Трасса Моспорт-Парк (3957 м) Дистанция 80 кругов, 316,560 км Погода Холодно, сухо Поул 1:13,188 (194,638 км/ч) Эмерсон ФиттипальдиMcLaren-Ford Быстрый круг 1:13,659 (193,394 км/ч)60-й круг Ники ЛаудаFerrari Подиум Побед�...

1875 Maryland gubernatorial election

Election for governor of Maryland, U.S. 1875 Maryland gubernatorial election ← 1871 November 2, 1875 1879 →   Nominee John Lee Carroll James Morrison Harris Party Democratic Republican Popular vote 85,454 72,530 Percentage 54.09% 45.91% Governor before election James Black Groome Democratic Elected Governor John Lee Carroll Democratic Elections in Maryland Federal government Presidential elections 1788–89 1792 1796 1800 1804 1808 1812 1816 1820 1824 1828 1832...

 

History of the hippie movement

Historical Record of the Hippie movement See also: History of subcultures in the 20th century and History of the United States (1964–1980) The hippie subculture (also known as the flower people) began its development as a youth movement in the United States during the early 1960s and then developed around the world. Its origins may be traced to European social movements in the 19th and early 20th century such as Bohemians, with influence from Eastern religion and spirituality. It is directl...

 

بوابة:أستراليا

أستراليا بوابة ويكيبيديا حول إحدى دول الكومنولث هي دولة تقع في نصف الكرة الجنوبي عند جنوب شرق آسيا على غرب المحيط الهادي، عاصمتها كانبرا. ويحيط القارة من الشمال بحر تيمور وبحر أرفورا ومضيق تورز وبالشرق بحر كورال وبحر تسمان وبالجنوب ممر باس، ويحيط بها من الجنوب والغرب المح...

Javier Viveros

Javier Viveros Información personalNacimiento 13 de septiembre de 1977 (46 años) Asunción, ParaguayNacionalidad ParaguayaEducaciónEducado en Universidad Nacional de Asunción Información profesionalOcupación EscritorAños activo siglo XXIGéneros Cuento, poesía, literatura infantil, historieta, teatro, cineObras notables Manual de esgrima para elefantes, Fantasmario, Urbano, demasiado urbano, Réquiem del Chaco, Páginas de hierroSitio web Blog oficialDistinciones Finalista d...

 

Gerd von Rundstedt

Dieser Artikel behandelt den Generalfeldmarschall im Zweiten Weltkrieg. Zum Generalmajor und Vater von diesem siehe Gerd von Rundstedt (Generalmajor). Gerd von Rundstedt 1940 nach seiner Ernennung zum Generalfeldmarschall Das Grab von Gerd von Rundstedt und seiner Ehefrau Luise geborene von Götz auf dem Stadtfriedhof Stöcken in Hannover Karl Rudolf Gerd von Rundstedt (* 12. Dezember 1875 in Aschersleben, Provinz Sachsen; † 24. Februar 1953 in Hannover) war ein deutscher Offizier, zuletzt...