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Brownian Excursion
In probability theory a Brownian excursion process is a stochastic process that is closely related to a Wiener process (or Brownian motion). Realisations of Brownian excursion processes are essentially just realizations of a Wiener process selected to satisfy certain conditions. In particular, a Brownian excursion process is a Wiener process conditioned to be positive and to take the value 0 at time 1. Alternatively, it is a Brownian bridge process conditioned to be positive. BEPs are important because, among other reasons, they naturally arise as the limit process of a number of conditional functional central limit theorems. Definition A Brownian excursion process, e, is a Wiener process (or Brownian motion) conditioned to be positive and to take the value 0 at time 1. Alternatively, it is a Brownian bridge process conditioned to be positive. Another representation of a Brownian excursion e in terms of a Brownian motion process ''W'' (due to Paul Lévy and note ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kai Lai Chung
Kai Lai Chung (traditional Chinese: 鍾開萊; simplified Chinese: 钟开莱; September 19, 1917 – June 2, 2009) was a Chinese-American mathematician known for his significant contributions to modern probability theory. Biography Chung was a native of Hangzhou, the capital city of Zhejiang Province. Chung entered Tsinghua University in 1936, and initially studied physics at its Department of Physics. In 1940, Chung graduated from the Department of Mathematics of the National Southwestern Associated University, where he later worked as a teaching assistant. During this period, he first studied number theory with Lo-Keng Hua and then probability theory with Pao-Lu Hsu. In 1944, Chung was chosen to be one of the recipients of the 6th Boxer Indemnity Scholarship Program for study in the United States. He arrived at Princeton University in December 1945 and obtained his PhD in 1947. Chung's dissertation was titled “On the maximum partial sum of sequences of independent ran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brownian Meander
In the mathematical theory of probability, Brownian meander W^+ = \ is a continuous non-homogeneous Markov process defined as follows: Let W = \ be a standard one-dimensional Brownian motion, and \tau := \sup \ , i.e. the last time before ''t'' = 1 when W visits \. Then the Brownian meander is defined by the following: :W^+_t := \frac 1 , W_ , , \quad t \in ,1 In words, let \tau be the last time before 1 that a standard Brownian motion visits \. (\tau < 1 almost surely.) We snip off and discard the trajectory of Brownian motion before , and scale the remaining part so that it spans a time interval of length 1. The scaling factor for the spatial axis must be square root of the scaling factor for the time axis. The process resulting from this snip-and-scale procedure is a Brownian meander. As the name suggests, it is a piece of Brownian motion that spends all its time away from its starting point . The [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Svante Janson
Carl Svante Janson (born 21 May 1955) is a Swedish mathematician. A member of the Royal Swedish Academy of Sciences since 1994, Janson has been the chaired professor of mathematics at Uppsala University since 1987. In mathematical analysis, Janson has publications in functional analysis (especially harmonic analysis) and probability theory. In mathematical statistics, Janson has made contributions to the theory of U-statistics. In combinatorics, Janson has publications in probabilistic combinatorics, particularly random graphs and in the analysis of algorithms: In the study of random graphs, Janson introduced U-statistics and the Hoeffding decomposition. Janson has published four books and over 300 academic papers (). He has an Erdős number of 1. Biography Svante Janson has already had a long career in mathematics, because he started research at a very young age. From prodigy to docent A child prodigy in mathematics, Janson took high-school and even university classes whil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Confluent Hypergeometric Function
In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities merge into an irregular singularity. The term ''confluent'' refers to the merging of singular points of families of differential equations; ''confluere'' is Latin for "to flow together". There are several common standard forms of confluent hypergeometric functions: * Kummer's (confluent hypergeometric) function , introduced by , is a solution to Kummer's differential equation. This is also known as the confluent hypergeometric function of the first kind. There is a different and unrelated Kummer's function bearing the same name. * Tricomi's (confluent hypergeometric) function introduced by , sometimes denoted by , is another solution to Kummer's equation. This is also known as the confluent hypergeometric function of the second kind. * Whittaker functions (for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Graph Theory
The ''Journal of Graph Theory'' is a peer-reviewed mathematics journal specializing in graph theory and related areas, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. It is published by John Wiley & Sons. The journal was established in 1977 by Frank Harary.Frank Harary a biographical sketch at the ACM site The are [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson Process
In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field. This point process has convenient mathematical properties, which has led to its being frequently defined in Euclidean space and used as a mathematical model for seemingly random processes in numerous disciplines such as astronomy,G. J. Babu and E. D. Feigelson. Spatial point processes in astronomy. ''Journal of statistical planning and inference'', 50(3):311–326, 1996. biology,H. G. Othmer, S. R. Dunbar, and W. Alt. Models of dispersal in biological systems. ''Journal of mathematical biology'', 26(3):263–298, 1988. ecology,H. Thompson. Spatial point processes, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kiyoshi Itō
Kiyoshi, (きよし or キヨシ), is a Japanese given name, also spelled Kyoshi. Possible meanings *'' Kyōshi'', a form of Japanese poetry *Kyōshi, a Japanese honorific Possible writings *清, "cleanse" *淳, "pure" *潔, "undefiled" *清志, "cleanse, intention" *清司, "cleanse, official" *聖, "holy" *澄, "lucidity" *潔司, "undefiled, official" People with the name * Akira Kawabata ("Kiyoshi"), pro wrestler *, Japanese sport wrestler *, Japanese pole vaulter *, Japanese film actor *, Japanese baseball player *, Japanese ice hockey player *, Japanese ice hockey player *, Japanese admiral *, Japanese artist *, Japanese Enka singer *, Japanese historian and Shinto priest *, Japanese drummer of Asian Kung-Fu Generation *, a Shiatsu Master, Shiatsupractor (SPR), *, Japanese academic, historian and writer *, Japanese mathematician *, Japanese general soldier *, Japanese Christian journalist *, Japanese voice actor *, Japanese businessman *, Japanese actor *, Japanese photogra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplace Transform
In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform In mathematics, an integral transform maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily characterized and manipulated than in ... that converts a Function (mathematics), function of a Real number, real Variable (mathematics), variable (usually t, in the ''time domain'') to a function of a Complex number, complex variable s (in the complex frequency domain, also known as ''s''-domain, or s-plane). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms ordinary differential equations into algebraic equations and convolution into multiplication. For suitable functions ''f'', the Laplace transform is the integral \mathcal\(s) = \int_0^\infty f(t)e^ \, dt. H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henry McKean
Henry P. McKean, Jr. (born 1930 in Wenham, Massachusetts) is an American mathematician at the Courant Institute in New York University. He works in various areas of mathematical analysis, analysis. He obtained his Doctor of Philosophy, PhD in 1955 from Princeton University under William Feller. He was elected to the National Academy of Sciences in 1980. In 2007 he was awarded the Leroy P. Steele Prize for his life's work. In 1978 he was an invited speaker at the International Congress of Mathematicians in Helsinki (''Algebraic curves of infinite genus arising in the theory of nonlinear waves''). In 2012 he became a fellow of the American Mathematical Society. His doctoral students include Michael Arbib, Luigi Chierchia, Harry Dym, Daniel Stroock, Eugene Trubowitz, Victor Moll and Pierre van Moerbeke and Uri Keich. Works Selected articles * * * * * * * Books *with Kiyosi Itô: ''Diffusion processes and their sample paths.'' Springer 1965. *''Stochastic Integrals.'' New York 1969. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory 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 expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kiyosi Itô
was a Japanese mathematician who made fundamental contributions to probability theory, in particular, the theory of stochastic processes. He invented the concept of stochastic integral and stochastic differential equation, and is known as the founder of so-called Itô calculus. Overview Itô pioneered the theory of stochastic integration and stochastic differential equations, now known as Itô calculus. Its basic concept is the Itô integral, and among the most important results is a change of variable formula known as Itô's lemma. Itô calculus is a method used in the mathematical study of random events and is applied in various fields, and is perhaps best known for its use in mathematical finance. Itô also made contributions to the study of diffusion processes on manifolds, known as stochastic differential geometry. Although the standard Hepburn romanization of his name is ''Kiyoshi Itō'', he used the spelling Kiyosi Itô (Kunrei-shiki romanization). The alternative ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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