Paul-André Meyer
Encyclopedia
Paul-André Meyer 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.
He is best known for his continuous-time analog of Doob's decomposition of a submartingale, known as the Doob–Meyer decomposition.
Some of his main areas of research in probability theory
were the general theory of stochastic processes, Markov process
es, stochastic integration, stochastic differential geometry and quantum probability
. His most cited book is Probabilities and Potential B, written with C. Dellacherie.
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
es, especially Markov process
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 has created an annual prize in memory of the mathematician Paul André Meyer.
The first IRMA Paul André Meyer prize was awarded in 2004http://www.ams.org/notices/200405/people.pdf.
Persi Diaconis
of Stanford University
wrote about Meyer that
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, 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.
He is best known for his continuous-time analog of Doob's decomposition of a submartingale, known as the Doob–Meyer decomposition.
Some of his main areas of research in probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
were the general theory of stochastic processes, Markov process
Markov process
In probability theory and statistics, a Markov process, named after the Russian mathematician Andrey Markov, is a time-varying random phenomenon for which a specific property holds...
es, stochastic integration, stochastic differential geometry and quantum probability
Quantum probability
Quantum probability was developed in the 1980s as a noncommutative analog of the Kolmogorovian theory of stochastic processes. One of its aims is to clarify the mathematical foundations of quantum theory and its statistical interpretation....
. His most cited book is Probabilities and Potential B, written with C. Dellacherie.
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
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
es, especially Markov process
Markov process
In probability theory and statistics, a Markov process, named after the Russian mathematician Andrey Markov, is a time-varying random phenomenon for which a specific property holds...
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 has created an annual prize in memory of the mathematician Paul André Meyer.
The first IRMA Paul André Meyer prize was awarded in 2004http://www.ams.org/notices/200405/people.pdf.
Persi Diaconis
Persi Diaconis
Persi Warren Diaconis is an American mathematician and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University....
of Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
wrote about Meyer that
- 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.
External links
- In memory of P. A. Meyer
- Colloque international sur les processus stochastiques et l’héritage de P.A. Meyer
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.