The stochastic is an English adjective that describes something randomly specified. The word first appears in English to describe mathematical objects called stochastic processes, but now in mathematics the terms stochastic and random processes are considered to be interchangeable. The word, with the current definition meaning random, comes from the German language, but the original comes from the Greek ?????? (stokhos) , which means 'aiming, guessing'.
The term stochastic is used in many fields, especially where stochastic or random processes are used to represent a system or phenomenon that seems to change randomly. Examples of such fields include the physical sciences such as biology, chemistry, ecology, neuroscience, and physics as well as areas of technology and techniques such as image processing, signal processing, information theory, computer science, cryptography and telecommunications. It is also used in finance, due to seemingly random changes in financial markets.
Video Stochastic
Etymology
The English stochastic was originally used as an adjective with the "alleged" definition, and derived from the Greek word meaning "targeting the mark, guess", and the Oxford English Dictionary gave the year 1662 the most early. In his work on the probability of Ars Conjectandi , originally published in Latin in 1713, Jakob Bernoulli uses the phrase "Ars Conjectandi sive Stochastice", which has been translated into "the art of speculation or stochastics". This sentence is used, with reference to Bernoulli, by Ladislaus Bortkiewicz who in 1917 wrote in German the word stochastic with the meaning of random meaning. The term stochastic process first appeared in English on paper 1934 by Joseph Doob. For certain mathematical terms and definitions, Doob quotes another 1934 paper, in which the term "stochasticcher ProzeÃÆ'Ÿ" is used in German by Aleksandr Khinchin, although the German term was used earlier in 1931 by Andrey Kolmogorov. Maps Stochastic
Math
In the early 1930s, Aleksandr Khinchin gave the first mathematical definition of stochastic processes as a set of random variables indexed by a real line. Further fundamental work on probability theory and stochastic processes is done by Khinchin and other mathematicians such as Andrey Kolmogorov, Joseph Doob, William Feller, Maurice Frà © Ã… © chet, Paul Là © vy, Wolfgang Doeblin, and Harald Cramà © r. The later decade of CramÃÆ'  © r was called 1930 as the "heroic period of mathematical probability theory".
In mathematics, in particular probability theory, the theory of stochastic processes is considered to be an important contribution to mathematics and continues to be an active research topic for both theoretical and application reasons.
The word stochastic is used to describe other terms and objects in mathematics. Examples include the stochastic matrix, which describes a stochastic process known as the Markov process, and stochastic calculus, involving differential and integral equations based on stochastic processes such as the Wiener process, also called the Brownian motion process.
Artificial Intelligence
In artificial intelligence, stochastic programs work by using probabilistic methods to solve problems, such as in annealing simulations, stochastic nerve tissues, stochastic optimization, genetic algorithms, and genetic programming. The problem itself may be stochastic as well, as in planning under uncertainty.
Nature Sciences
One of the simplest continuous stochastic processes is Brownian motion. It was first observed by botanist Robert Brown while looking through a microscope on pollen in water.
Physics
The name "Monte Carlo" for the Stochastic Monte Carlo method was popularized by Stanis physics researchers? Aw Ulam, Enrico Fermi, John von Neumann, and Nicholas Metropolis, among others. His name is a reference to Monte Carlo Casino in Monaco where Uncle Ulam will borrow money to gamble. The use of randomness and recurring properties of the process is analogous to the activities undertaken in the casino. Simulation methods and statistical sampling generally do the opposite: using a simulation to test a previously determined deterministic problem. Although the "reversed" examples of approach do exist historically, they are not considered a common method until the popularity of the Monte Carlo method spreads.
Perhaps the most famous early use was by Enrico Fermi in 1930, when he used a random method to calculate the properties of newly discovered neutrons. The Monte Carlo method is essential for the simulations needed for the Manhattan Project, although it is severely constrained by computing tools at the time. Therefore, only after the first electronic computer was built (starting in 1945), the Monte Carlo method began to be studied in depth. In the 1950s they were used at Los Alamos for early work related to the development of hydrogen bombs, and became popular in the fields of physics, physical chemistry, and operations research. The RAND Corporation and the US Air Force are the two major organizations responsible for funding and disseminating information about Monte Carlo methods during this time, and they are beginning to find broad applications in various fields.
The use of the Monte Carlo method requires a large number of random numbers, and that is the use of which spurs the development of pseudorandom number generators, which are much faster to use than the random number tables previously used for statistical sampling.
Biology
Stochastic resonance: In biological systems, introducing stochastic "noise" has been found to help increase the signal strength of the internal feedback loop for balance and other vestibular communications. It has been found to help diabetic patients and stroke with balance control. Many biochemical events also allow stochastic analysis. Gene expression, for example, has a stochastic component through molecular collisions - such as during binding and not binding to RNA polymerase to the gene promoter - through the Brownian motion of the solution.
Medicine
Stochastic effects, or "coincidental effects" are one classification of the effects of radiation that refers to the random nature, statistics of the damage. In contrast to the deterministic effect, the severity does not depend on the dose. Only the probability of an effect increases with the dose.
Geomorphology
The formation of river meanders has been analyzed as a stochastic process.
Creativity
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Computer science
Stochastic ray tracking is a Monte Carlo simulation application to computer graphics ray graphics algorithms. "Distributed ray sample tracking is integrated at many randomly selected points and average results to get a better approach.This is basically an application of the Monte Carlo method for 3D computer graphics, and for this reason it is also called tracking Stochastic rays . "
Stochastic forensics analyzes computer crime by viewing the computer as a stochastic process.
Music
In music, a probabilistic mathematical process can produce stochastic elements.
Stochastic processes can be used in music to compose fixed pieces or can be produced in performance. Stochastic music was spearheaded by Iannis Xenakis, who coined the term stochastic music . The specific examples of mathematics, statistics, and physics applied to musical compositions are the use of statistical gas mechanics in Pithoprakta, the distribution of dot stats in fields in Diamorphoses , minimal constraints in Achorripsis , normal distribution in ST/10 and AtrÃÆ'  © es , Markov chains in Analogiques , game theory in Duel and Stratà © gie , group theory in Nomos Alpha (for Siegfried Palm), set theory at Herma and Eonta , and the Brownian movement at N'Shima . Xenakis often uses computers to generate scores, such as the ST series including Morsima-Amorsima and AtrÃÆ'  © es , and set up CEMAMu. Previously, John Cage and others had composed aleatoric or indeterminate music, created by accidental processes but had no strict mathematical foundations (Cage's Music of Changes , for example, using chart system based on I-Ching ). Lejaren Hiller and Leonard Issacson used generative grammars and Markov chains in 1957 Illiac Suite . View: Generative music.
Subtractive color reproduction
When color reproduction is made, the image is separated into its component color by taking a few photos that are filtered for each color. One film or plate produced represents each data cyan, magenta, yellow, and black. Color printing is a binary system, in which the ink is present or not, so all the color separations to be printed must be translated into dots at some stage of the workflow. The traditional amplitude-modulated line display has problems with moirÃÆ'Â © but is used until stochastic screening becomes available. The stochastic dot pattern (or modulated frequency) creates a sharper image.
Language and linguistics
The non-deterministic approach in language study is largely inspired by the work of Ferdinand de Saussure, for example, in functionalist linguistic theory, which argues that competence is based on performance. The differences in functional grammar theory must be carefully distinguished from the distinction of langue and parole . As long as linguistic knowledge is grounded by experience with language, grammar is said to be probabilistic and variable rather than fixed and absolute. This grammatical conception as probabilistic and variable follows from the idea that one's competence changes according to one's experience with language. Although this conception has been contested, it also provides a foundation for the natural language processing of modern statistics and for the theory of language learning and change.
Social science
Stochastic social science theory is similar to system theory in that event is the interaction of the system, although with a clear emphasis on the unconscious process. The incident creates its own probable state, making it unpredictable if only for the number of variables involved. Stochastic social science theory can be seen as an elaboration of a kind of 'third axis' in which to place human behavior in addition to the traditional 'opposition' nurture opposition. See Julia Kristeva on her use of 'semiotics', Luce Irigaray on the inverted Heideggerian epistemology, and Pierre Bourdieu in the polythetic room for the example of stochastic social science theory.
Business
Manufacturing
The manufacturing process is assumed to be a stochastic process. This assumption is mostly applicable to sustainable manufacturing processes or batches. Testing and process monitoring are recorded using a process control chart that plots the process control parameters that are given over time. Usually a dozen or more parameters will be tracked simultaneously. Statistical models are used to determine the boundary line that determines when corrective action should be taken to bring the process back to the intended operational window.
This same approach is used in the service industry where parameters are replaced by processes associated with service level agreements.
Financial
Financial markets use stochastic models to represent random-looking asset behaviors such as stocks, commodities, relative currency prices (ie, the price of one currency versus other currencies, such as US Dollar prices versus the Euro currency), and interest rates. These models are then used by quantitative analysts to assess options on stock prices, bond prices, and interest rates, see the Markov model. Moreover, it is the heart of the insurance industry.
Media
Marketing and changes in the movements of the tastes and preferences of the audience, as well as the solicitation and scientific appeal of certain film and television debuts (ie, opening weekends, word-of-mouth, top-of-mind knowledge among groups surveyed, and other elements of social media outreach and advertising, determined in part by stochastic modeling.The latest attempt at repeated business analysis is done by Japanese scholars and is part of the Catalematic Transmission System patented by Geneva Media Holdings, and the modeling has been used in collecting data from when Nielsen's original assessment to a modern studio and television test audience.
See also
- Stochastic
- The jump process
- Sorting
Note
References
Further reading
- See the 8ft (2.4m) Probable Probability Stitching process that compares the stock market returns to randomly falling seeds through the quincunx pattern on YouTube. from the IFA.com Fund Index Adviser
- Formal Music: Thought and Mathematics in Composition by Iannis Xenakis, ISBNÃ, 1-57647-079-2
- The Frequency and Occurrence of Linguistic Structures by Joan Bybee and Paul Hopper (eds.), ISBNÃ, 1-58811-028-1/ISBNÃ, 90-272-2948-1 (Eur.)
- The Stitching and Weeding Model of Stochastic Emping provides documentation and computer code for modeling stochastic processes in Visual Basic for Applications.
External links
- The dictionary definition of stochastic in Wiktionary
Source of the article : Wikipedia
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