Stochastic
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Stochastic (
Stochasticity is used in many different fields, including the
Etymology
The word stochastic in English was originally used as an adjective with the definition "pertaining to conjecturing", and stemming from a Greek word meaning "to aim at a mark, guess", and the Oxford English Dictionary gives the year 1662 as its earliest occurrence.
Mathematics
In the early 1930s, Aleksandr Khinchin gave the first mathematical definition of a stochastic process as a family of random variables indexed by the real line.
In mathematics, the theory of stochastic processes is an important contribution to probability theory,[29] and continues to be an active topic of research for both theory and applications.[30][31][32]
The word stochastic is used to describe other terms and objects in mathematics. Examples include a
Natural science
One of the simplest continuous-time stochastic processes is Brownian motion. This was first observed by botanist Robert Brown while looking through a microscope at pollen grains in water.
Physics
The Monte Carlo method is a stochastic method popularized by physics researchers Stanisław Ulam, Enrico Fermi, John von Neumann, and Nicholas Metropolis.[33] The use of randomness and the repetitive nature of the process are analogous to the activities conducted at a casino. Methods of simulation and statistical sampling generally did the opposite: using simulation to test a previously understood deterministic problem. Though examples of an "inverted" approach do exist historically, they were not considered a general method until the popularity of the Monte Carlo method spread.
Perhaps the most famous early use was by Enrico Fermi in 1930, when he used a random method to calculate the properties of the newly discovered
Uses of Monte Carlo methods require large amounts of random numbers, and it was their use that spurred the development of pseudorandom number generators, which were far quicker to use than the tables of random numbers which had been previously used for statistical sampling.
Biology
Creativity
Simonton (2003, Psych Bulletin) argues that creativity in science (of scientists) is a constrained stochastic behaviour such that new theories in all sciences are, at least in part, the product of a stochastic process.[36]
Computer science
Stochastic forensics analyzes computer crime by viewing computers as stochastic steps.
In
. A problem itself may be stochastic as well, as in planning under uncertainty.Finance
The financial markets use stochastic models to represent the seemingly random behaviour of various financial assets, including the random behavior of the price of one currency compared to that of another (such as the price of US Dollar compared to that of the Euro), and also to represent random behaviour of
Geomorphology
The formation of river meanders has been analyzed as a stochastic process.
Language and linguistics
Non-deterministic approaches in language studies are largely inspired by the work of
Manufacturing
Manufacturing processes are assumed to be
This same approach is used in the service industry where parameters are replaced by processes related to service level agreements.
Media
The marketing and the changing movement of audience tastes and preferences, as well as the solicitation of and the scientific appeal of certain film and television debuts (i.e., their opening weekends, word-of-mouth, top-of-mind knowledge among surveyed groups, star name recognition and other elements of social media outreach and advertising), are determined in part by stochastic modeling. A recent attempt at repeat business analysis was done by Japanese scholars[
Medicine
Stochastic effect, or "chance effect" is one classification of radiation effects that refers to the random, statistical nature of the damage. In contrast to the deterministic effect, severity is independent of dose. Only the probability of an effect increases with dose.
Music
In music, mathematical processes based on probability can generate stochastic elements.
Stochastic processes may be used in music to compose a fixed piece or may be produced in performance. Stochastic music was pioneered by
Social sciences
Stochastic social science theory is similar to systems theory in that events are interactions of systems, although with a marked emphasis on unconscious processes. The event creates its own conditions of possibility, rendering it unpredictable if simply 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 situate human behavior alongside the traditional 'nature vs. nurture' opposition. See Julia Kristeva on her usage of the 'semiotic', Luce Irigaray on reverse Heideggerian epistemology, and Pierre Bourdieu on polythetic space for examples of stochastic social science theory.[citation needed]
The term stochastic terrorism has come into frequent use
Author David Neiwert, who wrote the book Alt-America, told Salon interviewer Chauncey Devega:
Scripted violence is where a person who has a national platform describes the kind of violence that they want to be carried out. He identifies the targets and leaves it up to the listeners to carry out this violence. It is a form of terrorism. It is an act and a social phenomenon where there is an agreement to inflict massive violence on a whole segment of society. Again, this violence is led by people in high-profile positions in the media and the government. They're the ones who do the scripting, and it is ordinary people who carry it out.
Think of it like Charles Manson and his followers. Manson wrote the script; he didn't commit any of those murders. He just had his followers carry them out.[45]
Subtractive color reproduction
When color reproductions are made, the image is separated into its component colors by taking multiple photographs filtered for each color. One resultant film or plate represents each of the cyan, magenta, yellow, and black data.
See also
Notes
References
- ^ a b c d "Stochastic". Lexico UK English Dictionary. Oxford University Press. Archived from the original on January 2, 2020.
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- ^ Applebaum, David (2004). "Lévy processes: From probability to finance and quantum groups". Notices of the AMS. 51 (11): 1336–1347.
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- ^ Douglas Hubbard "How to Measure Anything: Finding the Value of Intangibles in Business" p. 46, John Wiley & Sons, 2007
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- . In its most extreme form (Hopper 1987, 1988), USF rejects the Saussurean dichotomies such as langue vs. parôle. For early interpretivist approaches to focus, see Chomsky (1971) and Jackendoff (1972). parole and synchrony vs. diachrony. All adherents of this tendency feel that the Chomskyan advocacy of a sharp distinction between competence and performance is at best unproductive and obscurantist; at worst theoretically unmotivated. "
- ^ Bybee, Joan. "Usage-based phonology." p. 213 in Darnel, Mike (ed). 1999. Functionalism and Formalism in Linguistics: General papers. John Benjamins Publishing Company
- ^ Chomsky (1959). Review of Skinner's Verbal Behavior, Language, 35: 26–58
- ^ Manning and Schütze, (1999) Foundations of Statistical Natural Language Processing, MIT Press. Cambridge, MA
- ^ Bybee (2007) Frequency of use and the organization of language. Oxford: Oxford University Press
- ^ Ilias Chrissochoidis, Stavros Houliaras, and Christos Mitsakis, "Set theory in Xenakis' EONTA", in International Symposium Iannis Xenakis, ed. Anastasia Georgaki and Makis Solomos (Athens: The National and Kapodistrian University, 2005), 241–249.
- YouTube published August 12, 2019 CNN
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- ^ DeVega, Chauncey (1 November 2018). "Author David Neiwert on the outbreak of political violence". Salon. Retrieved 13 December 2018.
Further reading
- Formalized Music: Thought and Mathematics in Composition by ISBN 1-57647-079-2
- Frequency and the Emergence of Linguistic Structure by Joan Bybee and Paul Hopper (eds.), ISBN 90-272-2948-1(Eur.)
- The Stochastic Empirical Loading and Dilution Model provides documentation and computer code for modeling stochastic processes in Visual Basic for Applications.
External links
- The dictionary definition of stochastic at Wiktionary