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Skorokhod Space
Anatoliy Volodymyrovych Skorokhod ( uk, Анато́лій Володи́мирович Скорохо́д; September 10, 1930January 3, 2011) was a Soviet and Ukrainian mathematician. Skorokhod is well-known for a comprehensive treatise on the theory of stochastic processes, co-authored with Gikhman. In the words of mathematician and probability theorist Daniel W. Stroock “Gikhman and Skorokhod have done an excellent job of presenting the theory in its present state of rich imperfection.” Career Skorokhod worked at Kyiv University from 1956 to 1964. He was subsequently at the Institute of Mathematics of the National Academy of Sciences of Ukraine from 1964 until 2002. Since 1993, he had been a professor at Michigan State University in the US, and a member of the American Academy of Arts and Sciences. He was an academician of the National Academy of Sciences of Ukraine from 1985 to his death in 2011. His scientific works are on the theory of: * stochastic differential ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nikopol'
Nikopol ( uk, Ні́кополь ; from grc, Νικόπολις, lit=City of Victory) is a city and municipality ( hromada) in Nikopol District in the south of Ukraine, on the right bank of the Dnipro River, about 63 km south-east of Kryvyi Rih and 48 km south-west of Zaporizhzhia. Population: In terms of population, Nikopol is the fourth biggest city in the Dniopropetrovsk Oblast as well as among the top 50 nationwide. Located on a cape by the Kakhovka reservoir, Nikopol is a powerful industrial city which has several pipe producing factories (known for the Interpipe corporation), steel rolling mills (such as the factory of ferroalloys) and others. Renamed by the Russian Empire into Slaviansk and later Nikopol, the city has a rich preceding history being in 1638–1652 the settlement of Mykytyn Rih ( en, "Nikita Bend"), the capital of Zaporizhian Sich. It was one of the main crossings over the Dnipro river. Encyclopedia Britannica description The 1911 edit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
USSR
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national republics; in practice, both its government and its economy were highly centralized until its final years. It was a one-party state governed by the Communist Party of the Soviet Union, with the city of Moscow serving as its capital as well as that of its largest and most populous republic: the Russian SFSR. Other major cities included Leningrad (Russian SFSR), Kiev ( Ukrainian SSR), Minsk ( Byelorussian SSR), Tashkent (Uzbek SSR), Alma-Ata (Kazakh SSR), and Novosibirsk (Russian SFSR). It was the largest country in the world, covering over and spanning eleven time zones. The country's roots lay in the October Revolution of 1917, when the Bolsheviks, under the leadership of Vladimir Lenin, overthrew the Russian Provisional Gove ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a rando ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Process
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, cryptography and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance. Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion process ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Limit Theorem
In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. This theorem has seen many changes during the formal development of probability theory. Previous versions of the theorem date back to 1811, but in its modern general form, this fundamental result in probability theory was precisely stated as late as 1920, thereby serving as a bridge between classical and modern probability theory. If X_1, X_2, \dots, X_n, \dots are random samples drawn from a population with overall mean \mu and finite variance and if \bar_n is the sample mean of ... [...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 stocha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute Of Mathematical Statistics
The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts of the world. Beginning in 2005, the institute started offering joint membership with the Bernoulli Society for Mathematical Statistics and Probability as well as with the International Statistical Institute. The Institute was founded in 1935 with Harry C. Carver and Henry L. Rietz as its two most important supporters. The institute publishes a variety of journals, and holds several international conference every year. Publications The Institute publishes five journals: *'' Annals of Statistics'' *'' Annals of Applied Statistics'' *''Annals of Probability'' *'' Annals of Applied Probability'' *'' Statistical Science'' In addition, it co-sponsors: * The '' Current Index to Statistics'' * '' Electronic Communications in Probability'' * '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National Academy Of Sciences Of Ukraine
The National Academy of Sciences of Ukraine (NASU; uk, Національна академія наук України, ''Natsional’na akademiya nauk Ukrayiny'', abbr: NAN Ukraine) is a self-governing state-funded organization in Ukraine that is the main center of development of science and technology by coordinating a system of research institutes in the country. It is the main research oriented organization along with the five other academies in Ukraine specialized in various scientific disciplines. NAS Ukraine consists of numerous departments, sections, research institutes, scientific centers and various other supporting scientific organizations. The Academy reports on the annual basis to the Cabinet of Ministers of Ukraine. The presidium of the academy is located at vulytsia Volodymyrska, 57, across the street from the Building of Pedagogical Museum, which was used to host the Central Council during the independence period of 1917-18. In 1919–1991 it was a repu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academician
An academician is a full member of an artistic, literary, engineering, or scientific academy. In many countries, it is an honorific title used to denote a full member of an academy that has a strong influence on national scientific life. In systems such as the Academy of Sciences of the USSR, the title grants privileges and administrative responsibilities for funding allocation and research priorities. History Historically, the meaning for the title of ''Academician'' follows the traditions of the two most successful early scientific societies: either the Royal Society, where it was an honorary recognition by an independent body of peer reviewers and was meant to distinguish a person, while giving relatively little formal power, or the model of the French Academy of Sciences, which was much closer integrated with the government, provided with more state funding as an organization, and where the title of ''Academician'' implied in a lot more rights when it came to decision maki ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Academy Of Arts And Sciences
The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other Founding Fathers of the United States. It is headquartered in Cambridge, Massachusetts. Membership in the academy is achieved through a thorough petition, review, and election process. The academy's quarterly journal, ''Dædalus'', is published by MIT Press on behalf of the academy. The academy also conducts multidisciplinary public policy research. History The Academy was established by the Massachusetts legislature on May 4, 1780, charted in order "to cultivate every art and science which may tend to advance the interest, honor, dignity, and happiness of a free, independent, and virtuous people." The sixty-two incorporating fellows represented varying interests and high standing in the political, professional, and commercial s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taras Shevchenko National University Of Kyiv
Kyiv University or Shevchenko University or officially the Taras Shevchenko National University of Kyiv ( uk, Київський національний університет імені Тараса Шевченка), colloquially known as KNU, is located in Kyiv, the capital of Ukraine. The university is universally recognized as the most prestigious university of Ukraine, being the largest national higher education institution. KNU is ranked within top 650 universities in the world. It is the third oldest university in Ukraine after the University of Lviv and University of Kharkiv. Currently, its structure consists of fifteen faculties (academic departments) and five institutes. It was founded in 1834 by the Russian Tsar Nikolai I as the Saint Vladimir Imperial University of Kiev, and since then it has changed its name several times. During the Soviet Union era, Kiev State University was one of the top-three universities in the USSR, along with Moscow State University and L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel W
Daniel is a masculine given name and a surname of Hebrew origin. It means "God is my judge"Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxford University Press, 2nd edition, , p. 68. (cf. Gabriel—"God is my strength"), and derives from two early biblical figures, primary among them Daniel from the Book of Daniel. It is a common given name for males, and is also used as a surname. It is also the basis for various derived given names and surnames. Background The name evolved into over 100 different spellings in countries around the world. Nicknames (Dan, Danny) are common in both English and Hebrew; "Dan" may also be a complete given name rather than a nickname. The name "Daniil" (Даниил) is common in Russia. Feminine versions ( Danielle, Danièle, Daniela, Daniella, Dani, Danitza) are prevalent as well. It has been particularly well-used in Ireland. The Dutch names "Daan" and "Daniël" are also variations of Daniel. A related surname develop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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