Paul-André Meyer (21 August 1934 – 30 January 2003) was a French
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
, who played a major role in the development of the general theory of
stochastic processes
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stoc ...
.
He worked at the Institut de Recherche Mathématique (IRMA) in Strasbourg and is known as the founder of the 'Strasbourg school' in stochastic analysis.
Biography
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. He entered the
École Normale Supérieure
École or Ecole may refer to:
* an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing i ...
in 1954 where he studied mathematics. There, he attended lectures on probability by
Michel Loève
Michel Loève (; January 22, 1907 – February 17, 1979) was a French-American probability theory, probabilist and mathematical statistics, mathematical statistician, of Jewish origin. He is known in mathematical statistics and probability theory ...
, 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 process
In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, ...
es, 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
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
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...
were the general theory of
stochastic processes
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stoc ...
,
Markov process
In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, ...
es, stochastic integration, stochastic
differential geometry
Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...
and
quantum probability
The Born rule is a postulate of quantum mechanics that gives the probability that a measurement of a quantum system will yield a given result. In one commonly used application, it states that the probability density for finding a particle at a ...
. 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.
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 process
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Sto ...
es, especially
Markov process
In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, ...
es. 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 200
Persi Diaconis
Persi Warren Diaconis (; born January 31, 1945) is an American mathematician of Greek descent and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University.
He is particularly known f ...
of
Stanford University
Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...
wrote about Meyer that:
Some books and articles written by Paul-André Meyer
*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
External links
Colloque international sur les processus stochastiques et l’héritage de P.A. Meyer
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{{DEFAULTSORT:Meyer, Paul-Andre
French probability theorists
Members of the French Academy of Sciences
École Normale Supérieure alumni
20th-century French mathematicians
1934 births
2003 deaths