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Paul-André Meyer

December 15, 2023

Paul-André Meyer (21 August 1934 – 30 January 2003) was a French mathematician, who played a major role in the development of the general theory of stochastic processes. He worked at the Institut de Recherche Mathématique (IRMA) in Strasbourg and is known as the founder of the 'Strasbourg school' in stochastic analysis.

Paul-André Meyer
Born(1934-08-21)21 August 1934
Boulogne-Billancourt
Died30 January 2003(2003-01-30) (aged 68)
NationalityFrench
Alma materÉcole Normale Supérieure
Known forDoob-Meyer decomposition theorem
Theory of semimartingales
AwardsAmpère Prize (1982)
Scientific career
FieldsMathematics
InstitutionsInstitut de Recherche Mathématique
Doctoral advisorJacques Deny
Doctoral studentsDominique Bakry
Claude Dellacherie
Catherine Doléans-Dade

Biography edit

Meyer was born in 1934 in Boulogne, a suburb of Paris. His family fled from France in 1940 and sailed to Argentina, settling in Buenos Aires, where Paul-André attended a French school. He returned to Paris in 1946 and entered the Lycée Janson de Sailly, where he first encountered advanced mathematics through his teacher, M Heilbronn.[1] He entered the École Normale Supérieure in 1954 where he studied mathematics. There, he attended lectures on probability by Michel Loève, a former disciple of Paul Lévy who had come from Berkeley to spend a year in Paris. These lectures triggered Meyer's interest in the theory of stochastic processes, and he went on to write a thesis in potential theory, on multiplicative and additive functionals of Markov processes, under the supervision of Jacques Deny.

After his doctoral thesis, Meyer traveled to the United States and worked for a couple of years with the American mathematician Joseph Doob, who was then developing new ideas in the theory of stochastic processes. It was there that he derived his famous theorem on the decomposition of a submartingale, now known as the Doob–Meyer decomposition. After his return to France he established a group in Strasbourg where he ran his famous 'Séminaire de probabilités de Strasbourg', which became an epicenter for the development of the theory of stochastic processes in France for two decades.

Scientific work edit

Meyer is best known for his continuous-time analog of Doob's decomposition of a submartingale, known as the Doob–Meyer decomposition and his work on the 'general theory' of stochastic processes, published in his monumental book Probabilities and Potential, written with Claude Dellacherie.

Some of his main areas of research in probability theory were the general theory of stochastic processes, Markov processes, stochastic integration,[2] stochastic differential geometry and quantum probability. His most cited book is Probabilities and Potential B, written with Claude Dellacherie. The preceding book is the English translation of the second book in a series of five written by Meyer and Dellacherie from 1975 to 1992 and elaborated from Meyer's pioneering book Probabilités et Potentiel, published in 1966.[3][4][5]

In the period 1966-1980 Meyer organised the Seminaire de Probabilities in Strasbourg, and he and his co-workers developed what is called the general theory of processes.

This theory was concerned with the mathematical foundations of the theory of continuous time stochastic processes, especially Markov processes. Notable achievements of the 'Strasbourg School' were the development of stochastic integrals for semimartingales, and the concept of a predictable (or previsible) process.

IRMA created an annual prize in his memory; the first Paul André Meyer prize was awarded in 2004 [1].

Persi Diaconis of Stanford University wrote about Meyer that:[6]

I only met Paul-Andre Meyer once (at Luminy in 1995). He kindly stayed around after my talk and we spoke for about an hour. I was studying rates of convergence of finite state space Markov chains. He made it clear that, for him, finite state space Markov chains is a trivial subject. Hurt but undaunted, I explained some of our results and methods. He thought about it and said, “I see, yes, those are very hard problems”. The analytic parts of Dirichlet space theory have played an enormous role in my recent work. I am sure that there is much to learn from the abstract theory as well. In the present paper I treat rates of convergence for a simple Markov chain. I am sorry not to have another hour with Paul-Andre Meyer. Perhaps he would say “This piece of our story might help you”. Perhaps one of his students or colleagues can help fill the void.

Some books and articles written by Paul-André Meyer edit

  • C. Dellacherie, P.A. Meyer: Probabilities and Potential B, North-Holland, Amsterdam New York 1982.
  • P.A. Meyer: " Martingales and Stochastic Integrals I," Springer Lecture Notes in Mathematics 284, 1972.
  • Brelot's axiomatic theory of the Dirichlet problem and Hunt's theory, Annales de l'Institut Fourier, 13 no. 2 (1963), p. 357–372
  • Intégrales stochastiques I, Séminaire de probabilités de Strasbourg, 1 (1967), p. 72–94
  • Intégrales stochastiques II, Séminaire de probabilités de Strasbourg, 1 (1967), p. 95–117
  • Intégrales stochastiques III, Séminaire de probabilités de Strasbourg, 1 (1967), p. 118–141
  • Intégrales stochastiques IV, Séminaire de probabilités de Strasbourg, 1 (1967), p. 124–162
  • Generation of sigma-fields by step processes, Séminaire de probabilités de Strasbourg, 10 (1976), p. 118–124
  • P.A. Meyer: ' Inégalités de normes pour les integrales stochastiques," Séminaire de Probabilités XII, Springer Lecture Notes in Math. 649, 757–762, 1978.

References edit

  1. ^ "Paul-André Meyer - Biography".
  2. ^ Meyer, Paul-Andre (2002) [1976]. "Un cours sur les intégrales stochastiques". Séminaire de probabilités 1967–1980. Lect. Notes in Math. Vol. 1771. pp. 174–329. doi:10.1007/978-3-540-45530-1_11. ISBN 978-3-540-42813-8.
  3. ^ Bauer, Heinz (1968). "Review: Probabilities and potential, by P. A. Meyer". Bull. Amer. Math. Soc. 74 (1): 75–78. doi:10.1090/S0002-9904-1968-11880-4.
  4. ^ Getoor, Ronald (1980). "Review: Probabilities and potential, by C. Dellacherie and P. A. Meyer". Bull. Amer. Math. Soc. (N.S.). 2 (3): 510–514. doi:10.1090/s0273-0979-1980-14787-4.
  5. ^ Mitro, Joanna (1991). "Review: Probabilités et potentiel (Chapters XII – XVI), by C. Dellacherie and P. A. Meyer". Bull. Amer. Math. Soc. (N.S.). 24 (2): 471–477. doi:10.1090/s0273-0979-1991-16069-6.
  6. ^ Diaconis, Persi (2005). "Analysis of a Bose–Einstein Markov chain" (PDF). Annales de l'Institut Henri Poincaré B. 41 (3): 409–418. CiteSeerX 10.1.1.84.516. doi:10.1016/j.anihpb.2004.09.007.

External links edit

December 15, 2023
paul, andré, meyer, august, 1934, january, 2003, french, mathematician, played, major, role, development, general, theory, stochastic, processes, worked, institut, recherche, mathématique, irma, strasbourg, known, founder, strasbourg, school, stochastic, analy. Paul Andre Meyer 21 August 1934 30 January 2003 was a French mathematician who played a major role in the development of the general theory of stochastic processes He worked at the Institut de Recherche Mathematique IRMA in Strasbourg and is known as the founder of the Strasbourg school in stochastic analysis Paul Andre MeyerBorn 1934 08 21 21 August 1934Boulogne BillancourtDied30 January 2003 2003 01 30 aged 68 NationalityFrenchAlma materEcole Normale SuperieureKnown forDoob Meyer decomposition theoremTheory of semimartingalesAwardsAmpere Prize 1982 Scientific careerFieldsMathematicsInstitutionsInstitut de Recherche MathematiqueDoctoral advisorJacques DenyDoctoral studentsDominique BakryClaude DellacherieCatherine Doleans Dade Contents 1 Biography 2 Scientific work 3 Some books and articles written by Paul Andre Meyer 4 References 5 External linksBiography editMeyer was born in 1934 in Boulogne a suburb of Paris His family fled from France in 1940 and sailed to Argentina settling in Buenos Aires where Paul Andre attended a French school He returned to Paris in 1946 and entered the Lycee Janson de Sailly where he first encountered advanced mathematics through his teacher M Heilbronn 1 He entered the Ecole Normale Superieure in 1954 where he studied mathematics There he attended lectures on probability by Michel Loeve a former disciple of Paul Levy who had come from Berkeley to spend a year in Paris These lectures triggered Meyer s interest in the theory of stochastic processes and he went on to write a thesis in potential theory on multiplicative and additive functionals of Markov processes under the supervision of Jacques Deny After his doctoral thesis Meyer traveled to the United States and worked for a couple of years with the American mathematician Joseph Doob who was then developing new ideas in the theory of stochastic processes It was there that he derived his famous theorem on the decomposition of a submartingale now known as the Doob Meyer decomposition After his return to France he established a group in Strasbourg where he ran his famous Seminaire de probabilites de Strasbourg which became an epicenter for the development of the theory of stochastic processes in France for two decades Scientific work editMeyer is best known for his continuous time analog of Doob s decomposition of a submartingale known as the Doob Meyer decomposition and his work on the general theory of stochastic processes published in his monumental book Probabilities and Potential written with Claude Dellacherie Some of his main areas of research in probability theory were the general theory of stochastic processes Markov processes stochastic integration 2 stochastic differential geometry and quantum probability His most cited book is Probabilities and Potential B written with Claude Dellacherie The preceding book is the English translation of the second book in a series of five written by Meyer and Dellacherie from 1975 to 1992 and elaborated from Meyer s pioneering book Probabilites et Potentiel published in 1966 3 4 5 In the period 1966 1980 Meyer organised the Seminaire de Probabilities in Strasbourg and he and his co workers developed what is called the general theory of processes This theory was concerned with the mathematical foundations of the theory of continuous time stochastic processes especially Markov processes Notable achievements of the Strasbourg School were the development of stochastic integrals for semimartingales and the concept of a predictable or previsible process IRMA created an annual prize in his memory the first Paul Andre Meyer prize was awarded in 2004 1 Persi Diaconis of Stanford University wrote about Meyer that 6 I only met Paul Andre Meyer once at Luminy in 1995 He kindly stayed around after my talk and we spoke for about an hour I was studying rates of convergence of finite state space Markov chains He made it clear that for him finite state space Markov chains is a trivial subject Hurt but undaunted I explained some of our results and methods He thought about it and said I see yes those are very hard problems The analytic parts of Dirichlet space theory have played an enormous role in my recent work I am sure that there is much to learn from the abstract theory as well In the present paper I treat rates of convergence for a simple Markov chain I am sorry not to have another hour with Paul Andre Meyer Perhaps he would say This piece of our story might help you Perhaps one of his students or colleagues can help fill the void Some books and articles written by Paul Andre Meyer editC Dellacherie P A Meyer Probabilities and Potential B North Holland Amsterdam New York 1982 P A Meyer Martingales and Stochastic Integrals I Springer Lecture Notes in Mathematics 284 1972 Brelot s axiomatic theory of the Dirichlet problem and Hunt s theory Annales de l Institut Fourier 13 no 2 1963 p 357 372 Integrales stochastiques I Seminaire de probabilites de Strasbourg 1 1967 p 72 94 Integrales stochastiques II Seminaire de probabilites de Strasbourg 1 1967 p 95 117 Integrales stochastiques III Seminaire de probabilites de Strasbourg 1 1967 p 118 141 Integrales stochastiques IV Seminaire de probabilites de Strasbourg 1 1967 p 124 162 Generation of sigma fields by step processes Seminaire de probabilites de Strasbourg 10 1976 p 118 124 P A Meyer Inegalites de normes pour les integrales stochastiques Seminaire de Probabilites XII Springer Lecture Notes in Math 649 757 762 1978 References edit Paul Andre Meyer Biography Meyer Paul Andre 2002 1976 Un cours sur les integrales stochastiques Seminaire de probabilites 1967 1980 Lect Notes in Math Vol 1771 pp 174 329 doi 10 1007 978 3 540 45530 1 11 ISBN 978 3 540 42813 8 Bauer Heinz 1968 Review Probabilities and potential by P A Meyer Bull Amer Math Soc 74 1 75 78 doi 10 1090 S0002 9904 1968 11880 4 Getoor Ronald 1980 Review Probabilities and potential by C Dellacherie and P A Meyer Bull Amer Math Soc N S 2 3 510 514 doi 10 1090 s0273 0979 1980 14787 4 Mitro Joanna 1991 Review Probabilites et potentiel Chapters XII XVI by C Dellacherie and P A Meyer Bull Amer Math Soc N S 24 2 471 477 doi 10 1090 s0273 0979 1991 16069 6 Diaconis Persi 2005 Analysis of a Bose Einstein Markov chain PDF Annales de l Institut Henri Poincare B 41 3 409 418 CiteSeerX 10 1 1 84 516 doi 10 1016 j anihpb 2004 09 007 External links editIn memory of P A Meyer Colloque international sur les processus stochastiques et l heritage de P A Meyer Paul Andre Meyer at the Mathematics Genealogy Project Literature by and about Paul Andre Meyer in the German National Library catalogue Retrieved from https en wikipedia org w index php title Paul Andre Meyer amp oldid 1179857668, wikipedia, wiki, book, books, library,

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