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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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peng (surname)
Peng (Chinese: 彭; pinyin: Péng; alternative forms of romanization include Pang and Phang (Cantonese, Hakka), Pangestu or Pangestoe (Indonesian), and Bành (Vietnamese)) is a common Chinese family name, ranking 35th most common in 2006. It is the 47th name on the ''Hundred Family Surnames'' poem. Etymology The character (彭) is composed of (''zhǔ'' meaning "drum") and a pictograph (''shān'' representing "beats"). More commonly used as a surname, this character is also an adjective, meaning "big". Origin The surname Peng (彭) is traced to the legend of Peng Zu, God of Longevity, who legend tells lived 800 years. During the Shang dynasty, Jian Keng, a descendant of Zhuanxu, was granted the feudal territory Dapeng (Great Peng), and later adopted the name, Peng Zu. Distribution In 2019 it was the 31st most common surname in Mainland China. Of the top 30 cities in China, 彭 ranked 9th most common in the city of Changsha."https://www.douban.com/group/topic/23803598/"(Chi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People's Daily
The ''People's Daily'' () is the official newspaper of the Central Committee of the Chinese Communist Party (CCP). The newspaper provides direct information on the policies and viewpoints of the CCP. In addition to its main Chinese-language edition, the ''People's Daily'' is published in multiple languages. History The paper was established on 15 June 1948 and was published in Pingshan, Hebei, until its offices were moved to Beijing in March 1949. Ever since its founding, the ''People's Daily'' has been under direct control of the CCP's top leadership. Deng Tuo and Wu Lengxi served as editor-in-chief from 1948 to 1958 and 1958–1966, respectively, but the paper was in fact controlled by Mao Zedong's personal secretary Hu Qiaomu. During the Cultural Revolution, the ''People's Daily'' was one of the few sources of information from which either foreigners or Chinese could figure out what the Chinese government was doing or planning to do. During this period, an editorial in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamilton–Jacobi–Bellman Equation
In optimal control theory, the Hamilton-Jacobi-Bellman (HJB) equation gives a necessary and sufficient condition for optimality of a control with respect to a loss function. It is, in general, a nonlinear partial differential equation in the value function, which means its solution the value function itself. Once this solution is known, it can be used to obtain the optimal control by taking the maximizer (or minimizer) of the Hamiltonian involved in the HJB equation. The equation is a result of the theory of dynamic programming which was pioneered in the 1950s by Richard Bellman and coworkers. The connection to the Hamilton–Jacobi equation from classical physics was first drawn by Rudolf Kálmán. In discrete-time problems, the corresponding difference equation is usually referred to as the Bellman equation. While classical variational problems, such as the brachistochrone problem, can be solved using the Hamilton–Jacobi–Bellman equation, the method can be applied to a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equations
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity, and stability. Among the many open questions are the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feynman–Kac Formula
The Feynman–Kac formula, named after Richard Feynman and Mark Kac, establishes a link between parabolic partial differential equations (PDEs) and stochastic processes. In 1947, when Kac and Feynman were both Cornell faculty, Kac attended a presentation of Feynman's and remarked that the two of them were working on the same thing from different directions. The Feynman–Kac formula resulted, which proves rigorously the real case of Feynman's path integrals. The complex case, which occurs when a particle's spin is included, is still unproven. It offers a method of solving certain partial differential equations by simulating random paths of a stochastic process. Conversely, an important class of expectations of random processes can be computed by deterministic methods. Theorem Consider the partial differential equation :\frac(x,t) + \mu(x,t) \frac(x,t) + \tfrac \sigma^2(x,t) \frac(x,t) -V(x,t) u(x,t) + f(x,t) = 0, defined for all x \in \mathbb and t \in , T/math>, subject to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean-Michel Bismut
Jean-Michel Bismut (born 26 February 1948) is a French mathematician who has been a professor at the Université Paris-Sud since 1981. His mathematical career covers two apparently different branches of mathematics: probability theory and differential geometry. Ideas from probability play an important role in his works on geometry. Biography Bismut's early work was related to stochastic differential equations, stochastic control, and Malliavin calculus, to which he made fundamental contributions. Bismut received in 1973 his Docteur d'État in Mathematics, from the Université Paris-VI, a thesis entitled Analyse convexe et probabilités. In his thesis, Bismut established a stochastic version of Pontryagin's maximum principle in control theory by introducing and studying the backward stochastic differential equations which have been the starting point of an intensive research in stochastic analysis and it stands now as a major tool in Mathematical Finance. Using the quasi-i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Differential Equation
A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs are used to model various phenomena such as stock prices or physical systems subject to thermal fluctuations. Typically, SDEs contain a variable which represents random white noise calculated as the derivative of Brownian motion or the Wiener process. However, other types of random behaviour are possible, such as jump processes. Random differential equations are conjugate to stochastic differential equations. Background Stochastic differential equations originated in the theory of Brownian motion, in the work of Albert Einstein and Smoluchowski. These early examples were linear stochastic differential equations, also called 'Langevin' equations after French physicist Langevin, describing the motion of a harmonic oscillator subject to a random force. The mathematical theory of stochasti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 founded the Theory of Backward Stochastic differential equations A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs are used to model various phenomena such as stock pr .... 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] |
Optimal Control
Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure. Or the dynamical system could be a nation's economy, with the objective to minimize unemployment; the controls in this case could be fiscal and monetary policy. A dynamical system may also be introduced to embed operations research problems within the framework of optimal control theory. Optimal control is an extension of the calculus of variations, and is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and Richard Bellman in the 1950s, after contributions to calc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctorate
A doctorate (from Latin ''docere'', "to teach"), doctor's degree (from Latin ''doctor'', "teacher"), or doctoral degree is an academic degree awarded by universities and some other educational institutions, derived from the ancient formalism ''licentia docendi'' ("licence to teach"). In most countries, a research degree qualifies the holder to teach at university level in the degree's field or work in a specific profession. There are a number of doctoral degrees; the most common is the Doctor of Philosophy (PhD), awarded in many different fields, ranging from the humanities to scientific disciplines. In the United States and some other countries, there are also some types of technical or professional degrees that include "doctor" in their name and are classified as a doctorate in some of those countries. Professional doctorates historically came about to meet the needs of practitioners in a variety of disciplines. Many universities also award honorary doctorates to individuals d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacques-Louis Lions
Jacques-Louis Lions (; 3 May 1928 – 17 May 2001) was a French mathematician who made contributions to the theory of partial differential equations and to stochastic control, among other areas. He received the SIAM's John von Neumann Lecture prize in 1986 and numerous other distinctions.Jacques-Louis Lions Casinapioiv.va. Retrieved on 9 May 2016. isces.org Lions is listed as an . Biography After being part of the French Résistance in 1943 ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
