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Étienne Pardoux
Étienne Pardoux (born 1947) is a French mathematician working in the field of Stochastic analysis, in particular Stochastic partial differential equations. He is currently Professor at Aix-Marseille University. He obtained his PhD in 1975 at University of Paris-Sud under the supervision of Alain Bensoussan and Roger Meyer Temam. Together with Peng Shige, he developed the Theory of nonlinear Backward Stochastic Differential Equation A backward stochastic differential equation (BSDE) is a stochastic differential equation with a terminal condition in which the solution is required to be adapted with respect to an underlying filtration. BSDEs naturally arise in various applicat ...s (BSDE). References External links Aix-Marseille University faculty page 1947 births Living people French mathematicians Academic staff of Aix-Marseille University {{France-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Analysis
Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. This field was created and started by the Japanese mathematician Kiyosi Itô during World War II. The best-known stochastic process to which stochastic calculus is applied is the Wiener process (named in honor of Norbert Wiener), which is used for modeling Brownian motion as described by Louis Bachelier in 1900 and by Albert Einstein in 1905 and other physical diffusion processes in space of particles subject to random forces. Since the 1970s, the Wiener process has been widely applied in financial mathematics and economics to model the evolution in time of stock prices and bond interest rates. The main flavours of stochastic calculus are the Itô calculus and its variational relative the Malliavin calculus. For technical reasons the Itô integral is the mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Partial Differential Equations
Stochastic partial differential equations (SPDEs) generalize partial differential equations via random force terms and coefficients, in the same way ordinary stochastic differential equations generalize ordinary differential equations. They have relevance to quantum field theory, statistical mechanics, and spatial modeling. Examples One of the most studied SPDEs is the stochastic heat equation, which may formally be written as : \partial_t u = \Delta u + \xi\;, where \Delta is the Laplacian and \xi denotes space-time white noise. Other examples also include stochastic versions of famous linear equations, such as the wave equation and the Schrödinger equation. Discussion One difficulty is their lack of regularity. In one dimensional space, solutions to the stochastic heat equation are only almost 1/2-Hölder continuous in space and 1/4-Hölder continuous in time. For dimensions two and higher, solutions are not even function-valued, but can be made sense of as random di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aix-Marseille University
Aix-Marseille University (AMU; ; formally incorporated as ) is a Public university, public research university located in the Provence region of southern France. It was founded in 1409 when Louis II of Anjou, List of rulers of Provence, Count of Provence, petitioned the Council of Pisa, Pisan Antipope Alexander V to establish the University of Provence, making it one of the List of oldest universities in continuous operation, oldest university-level institutions in the Francophone world. The institution came into its current form following a reunification of the University of Provence, the University of the Mediterranean and Paul Cézanne University. The reunification became effective on 1 January 2012, resulting in the creation of the largest university in the List of countries and territories where French is an official language, French-speaking world in terms of its student body, its faculty and staff, and its budget that currently stands at €750 million. The university is or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Paris-Sud
Paris-Sud University (), also known as the University of Paris — XI (or as the Orsay Faculty of Sciences, University of Paris before 1971), was a French research university distributed among several campuses in the southern suburbs of Paris, including Orsay, Cachan, Châtenay-Malabry, Sceaux, Hauts-de-Seine, Sceaux, and Kremlin-Bicêtre campuses. In 2019, the university was replaced by the Paris-Saclay University. History Paris-Sud, as the Orsay Faculty of Sciences, was originally part of the University of Paris, which was subsequently split into several universities. After World War II, the rapid growth of nuclear physics and chemistry meant that research needed more and more powerful accelerators, which required large areas. The University of Paris, the and the looked for space in the south of Paris near Orsay. Later some of the teaching activity of the Faculty of Sciences in Paris was transferred to Orsay in 1956 at the request of Irène Joliot-Curie and Frédéric Joli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alain Bensoussan
Alain Bensoussan (born 12 May 1940) is a French mathematician. He is Professor Emeritus at the University of Paris-Dauphine and Professor at the University of Texas at Dallas. Early life and education Alain Bensoussan was born on 12 May 1940 in Tunis, Tunisia. Bensoussan is a former student of the École polytechnique (X1960), a graduate of ENSAE and a doctor of mathematics from the Faculty of Sciences in Paris (1969) under the supervision of Jacques-Louis Lions. Career He was a lecturer at the École polytechnique from 1970 to 1986 and a professor at the École normale supérieure from 1980 to 1985. He was Director of the European Institute for Advanced Studies in Management, Brussels from 1975 to 1977. He was President of INRIA from 1984 to 1996, President of the National Centre for Space Studies (CNES) from 1996 to 2003, President of the Council of the European Space Agency (ESA) from 1999 to 2002. Scientific works Alain Bensoussan's work has focused on automation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roger Meyer Temam
Roger Meyer Temam (born 19 May 1940) is a French mathematician and Professor of Mathematics at Indiana University Bloomington, working in the fields of numerical analysis, nonlinear partial differential equations and fluid mechanics. He is known for his contributions to the theory of the Navier–Stokes equations and to numerical analysis. He has published over 400 articles, as well as 12 (authored or co-authored) books. According to the ''Mathematics Genealogy Project'', Temam has also supervised 127 doctoral theses, the second-highest number supervised by an individual in the field of mathematics. He has a total of 654 mathematical "descendants," including Denis Serre. Life and education Roger Temam (Arabic: روجي تمام) was born in Tunis, into a Jewish family. He moved to France at the age of 17 and enrolled at the University of Paris – the Sorbonne to study Mathematics. In 1960, he became an assistant at the Faculty of Mechanics of the Faculty of Sciences of Pari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peng Shige
Peng Shige (, born December 8, 1947, in Binzhou, Shandong) is a Chinese mathematician noted for his contributions in stochastic analysis and mathematical finance. Biography Peng Shige was born in Binzhou and raised in Shandong, while his parents' hometown is Haifeng County in south-eastern Guangdong, he is a grandnephew of the famous revolutionary Peng Pai, and his grandfather (Peng Pai's brother) is also recognized a "revolutionary martyr" by the nation. He went to a countryside working with farmers as an " Educated youth" from 1968 to 1971, and studied in the Department of Physics, Shandong University from 1971 to 1974 and went to work at the Institute of Mathematics, Shandong University in 1978. In 1983 he took an opportunity to enter Paris Dauphine University, France, under the supervision of Alain Bensoussan, who was a student of Jacques-Louis Lions. He obtained his PhDs from Paris Dauphine University in 1985 and from University of Provence in 1986. Then he returned to Chi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backward Stochastic Differential Equation
A backward stochastic differential equation (BSDE) is a stochastic differential equation with a terminal condition in which the solution is required to be adapted with respect to an underlying filtration. BSDEs naturally arise in various applications such as stochastic control, mathematical finance, and nonlinear Feynman-Kac formula. Background Backward stochastic differential equations were introduced by Jean-Michel Bismut in 1973 in the linear case and by Étienne Pardoux and Shige Peng in 1990 in the nonlinear case. Mathematical framework Fix a terminal time T>0 and a probability space (\Omega,\mathcal,\mathbb). Let (B_t)_ be a Brownian motion with natural filtration (\mathcal_t)_. A backward stochastic differential equation is an integral equation of the type where f: ,Ttimes\mathbb\times\mathbb\to\mathbb is called the generator of the BSDE, the terminal condition \xi is an \mathcal_T-measurable random variable, and the solution (Y_t,Z_t)_ consists of stochastic proce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1947 Births
It was the first year of the Cold War, which would last until 1991, ending with the dissolution of the Soviet Union. Events January * January–February – Winter of 1946–47 in the United Kingdom: The worst snowfall in the country in the 20th century causes extensive disruption of travel. Given the low ratio of private vehicle ownership at the time, it is mainly remembered in terms of its effects on the railway network. * January 1 – The ''Canadian Citizenship Act, 1946, Canadian Citizenship Act'' comes into effect, providing a Canadian citizenship separate from British law. * January 4 – First issue of weekly magazine ''Der Spiegel'' published in Hanover, Germany, edited by Rudolf Augstein. * January 10 – The United Nations adopts a resolution to take control of the free city of Trieste. * January 15 – Elizabeth Short, an aspiring actress nicknamed the "Black Dahlia", is found brutally murdered in a vacant lot in Los Angeles; the mysterious case is never solv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Purpose: Because living persons may suffer personal harm from inappropriate information, we should watch their articles carefully. By adding an article to this category, it marks them with a notice about sources whenever someone tries to edit them, to remind them of WP:BLP (biographies of living persons) policy that these articles must maintain a neutral point of view, maintain factual accuracy, and be properly sourced. Recent changes to these articles are listed on Special:RecentChangesLinked/Living people. Organization: This category should not be sub-categorized. Entries are generally sorted by family name In many societies, a surname, family name, or last name is the mostly hereditary portion of one's personal name that indicates one's family. It is typically combined with a given name to form the full name of a person, although several give .... Maintenance: Individuals of advanced age (over 90), for whom there has been no new documentation in the last ten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
