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Daniel Revuz

Daniel Revuz
Born1936 (age 87–88)
NationalityFrench
Alma materThe Sorbonne
Known forRevuz correspondence
Revuz measure
Scientific career
FieldsProbability theory
InstitutionsParis 7
Thesis Mesures associées aux fonctionnelles additives de Markov  (1969)
Doctoral advisorJacques Neveu

Daniel Revuz (born 1936 in Paris) is a French mathematician specializing in probability theory, particularly in functional analysis applied to stochastic processes. He is the author of several reference works on Brownian motion, Markov chains, and martingales.

Family and early life

Revuz is the son of mathematicians Germaine and André Revuz [fr], and is one of six children. His family spent parts of his childhood in Poitiers and Istanbul before settling in Paris in 1950.[1]

Education and career

Revuz graduated from Polytechnique in 1956[2] and received his doctorate from the Sorbonne in 1969 under Jacques Neveu and Paul-André Meyer.[3] He taught at Paris Diderot University at the Laboratory for Probability Theory of the Institut Mathématique de Jussieu.[4]

Research

From his doctoral thesis work Revuz published two articles in 1970, in which he established a theory of one-to-one correspondence between positive Markov additive functionals and associated measures.[5][6] This theory and the associated measures are now known respectively as "Revuz correspondence" and "Revuz measures."[7]

In 1991 Revuz co-authored a research monograph with Marc Yor on stochastic processes and stochastic analysis called "Continuous Martingales and Brownian Motion". The book was highly praised upon its publication.[8] Wilfrid Kendall called it "the book for a capable graduate student starting out on research in probability."[9]

References

  1. ^ Hommage à André Revuz [Homage to André Revuz] (in French), LDAR - Paris Diderot University, retrieved 23 March 2024
  2. ^ "Graduate directory", ax.polytechnique.org, École Polytechnique Alumni, retrieved 23 March 2024
  3. ^ Daniel Revuz at the Mathematics Genealogy Project
  4. ^ Chincholle, Blandine (2014). "Archives de l'UFR de mathématiques de l'Université Paris Diderot (1965-2008)" [Archives of the Mathematics Department of the University of Paris Diderot (1965-2008)]. gouv.fr (in French). Retrieved 23 March 2024.
  5. ^ Revuz, Daniel (1970). "Mesures associées aux fonctionnelles additives de Markov I". Transactions of the American Mathematical Society (in French). 148 (2): 501–531. doi:10.2307/1995386. ISSN 0002-9947. Retrieved 23 March 2024.
  6. ^ Revuz, Daniel (1970). "Mesures associées aux fonctionnelles additives de Markov II". Wahrscheinlichkeitstheorie und Verwandte Gebiete (in French). 16 (4). Springer-Verlag: 336–344. doi:10.1007/BF00535137. ISSN 1432-2064. Retrieved 23 March 2024.
  7. ^ Li, Liping; Ying, Jiangang (2015). "Bivariate Revuz Measures and the Feynman-Kac Formula on Semi-Dirichlet Forms". Potential Analysis. 42: 775–808. arXiv:1504.04992. doi:10.1007/s11118-014-9457-y. ISSN 1572-929X. Retrieved 23 March 2024.
  8. ^ Reviews of Continuous martingales and Brownian motion:
  9. ^ Kendall, Wilfrid S. (1992). "Continuous Martingales and Brownian Motion". Bulletin of the London Mathematical Society. 24 (4): 410–413. doi:10.1112/blms/24.4.410.


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