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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] |
Cornell University
Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach and make contributions in all fields of knowledge—from the classics to the sciences, and from the theoretical to the applied. These ideals, unconventional for the time, are captured in Cornell's founding principle, a popular 1868 quotation from founder Ezra Cornell: "I would found an institution where any person can find instruction in any study." Cornell is ranked among the top global universities. The university is organized into seven undergraduate colleges and seven graduate divisions at its main Ithaca campus, with each college and division defining its specific admission standards and academic programs in near autonomy. The university also administers three satellite campuses, two in New York City and one in Education Ci ... [...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] |
Stochastic Integration
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 Kiyoshi 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 m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Issei Shiraishi And Kiyoshi Ito 1935
is a Japanese-language term used by ethnic Japanese in countries in North America and South America to specify the Japanese people who were the first generation to immigrate there. are born in Japan; their children born in the new country are (, "two", plus , "generation"); and their grandchildren are (, "three", plus , "generation"). The character and uniqueness of the is recognized in their social history. History The earliest organized group of Japanese emigrants settled in Mexico in 1897.Ministry of Foreign Affairs ''Japan-Mexico Foreign Relations''/ref> In the 21st century, the four largest populations of diaspora Japanese and descendants of Japanese immigrants in the Western Hemisphere live in Brazil, the United States, Canada, and Peru. Brazilian Brazil is home to the largest ethnic Japanese population outside Japan, numbering an estimated more than 1.5 million (including those of mixed-race or mixed-ethnicity), more than that of the 1.2 million in th ... [...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] |
Stochastic Integral
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 Kiyoshi 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 most ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic 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 Brownia ... [...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 prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hyp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Japanese People
The are an East Asian ethnic group native to the Japanese archipelago."人類学上は，旧石器時代あるいは縄文時代以来，現在の北海道〜沖縄諸島（南西諸島）に住んだ集団を祖先にもつ人々。" () Japanese people constitute 97.9% of the population of the country of Japan. Worldwide, approximately 129 million people are of Japanese descent; of these, approximately 122.5 million are residents of Japan. People of Japanese ancestry who live outside Japan are referred to as , the Japanese diaspora. Depending on the context, the term may be limited or not to mainland Japanese people, specifically the Yamato (as opposed to Ryukyuan and Ainu people). Japanese people are one of the largest ethnic groups in the world. In recent decades, there has also been an increase in the number of multiracial people with both Japanese and non-Japanese roots, including half Japanese people. History Theories of origins Archaeological evidence i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauss Prize
The Carl Friedrich Gauss Prize for Applications of Mathematics is a mathematics award, granted jointly by the International Mathematical Union and the German Mathematical Society for "outstanding mathematical contributions that have found significant applications outside of mathematics". The award receives its name from the German mathematician Carl Friedrich Gauss. With its premiere in 2006, it is to be awarded every fourth year, at the International Congress of Mathematicians. The previous laureate was presented with a medal and a cash purse of EUR10,000 funded by the International Congress of Mathematicians 1998 budget surplus. The official announcement of the prize took place on 30 April 2002, the 225th anniversary of the birth of Gauss. The prize was developed specifically to give recognition to mathematicians; while mathematicians influence the world outside of their field, their studies are often not recognized. The prize aims to honour those who have made contributions and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kyoto Prize
The is Japan's highest private award for lifetime achievement in the arts and sciences. It is given not only to those that are top representatives of their own respective fields, but to "those who have contributed significantly to the scientific, cultural, and spiritual betterment of mankind". The Kyoto Prize was created in collaboration with the Nobel Foundation and is regarded by many as Japan's version of the Nobel Prize, representing one of the most prestigious awards available in fields that are not traditionally honored with a Nobel. The prizes are endowed with 100 million yen (roughly 800,000 USD) per category and have been awarded annually since 1985 by the Inamori Foundation, founded by Kazuo Inamori. The laureates are announced each June; the prize presentation ceremony and related events are held in Kyoto, Japan, each November. Categories and fields The Kyoto Prize consists of three different categories, each with 4 subfields. The subfields rotate every year to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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