Stochastic
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'''''Stochastic''''', from the [[Greek language|Greek]] "Στόχος" which means "aim, guess", means of, relating to, or characterized by [[conjecture]] and [[randomness]].
A [[stochastic process]] is one whose behavior is non-[[deterministic]] in that a state does not fully determine its next state. Stochastic crafts are complex systems whose practitioners, even if complete experts, cannot guarantee success. Classical examples of this are [[medicine]]: a doctor can administer the same treatment to multiple patients suffering from the same symptoms, however, the patients may not all react to the treatment the same way. This makes medicine a stochastic process.<ref>Brad Inwood. Goal and Target in Stoicism [http://links.jstor.org/sici?sici=0022-362X(198610)83%3A10%3C547%3AGATIS%3E2.0.CO%3B2-0]. The Journal of Philosophy, Vol. 83, No. 10, Eighty-Third Annual Meeting American Philosophical Association, Eastern Division (Oct., 1986), pp. 547-556 doi:10.2307/2026429</ref> Additional examples are [[warfare]] and [[rhetoric]], where the successes and failures cannot be certainly predicted.
==Mathematical theory==
In [[mathematics]], specifically in [[probability theory]], the field of [[stochastic process]]es has for some decades been a major area of research. It is often assumed to be related to statistics; this is in fact a mistake, as stochastics are often used in physical systems. So studying stochastics is not the same as studying statistics.
A [[stochastic matrix]] is a [[matrix (mathematics)|matrix]] that has non-negative [[real number|real]] entries that sum to 1 in each row.
==Artificial intelligence==
In [[artificial intelligence]] stochastic programs work by using probabilistic methods to solve problems, as in [[simulated annealing]], [[Stochastic neural network|stochastic neural networks]], [[stochastic optimization]], and [[genetic algorithms]]. A problem itself may be stochastic as well, as in planning under uncertainty. A [[deterministic]] environment is much simpler for an agent to deal with.
==Natural science==
An example of a [[stochastic process]] in the natural world is [[pressure]] in a [[gas]] as modeled by the [[Wiener process]]. Even though (classically speaking) each molecule is moving in a deterministic path, the motion of a collection of them is computationally and practically unpredictable. A large enough set of molecules will exhibit stochastic characteristics, such as filling the container, exerting equal pressure, diffusing along concentration gradients,
etc. These are [[emergent property|emergent properties]] of the system.
===Biology===
*[[Stochastic resonance]]
In biological systems, introducing stochastic 'noise' has been found to help improve the signal strength of the internal feedback loops for balance and other vestibular communication. It has been found to help diabetic and stroke patients with balance control.<ref>Priplata A. et al. [http://www.bu.edu/abl/files/fulltext.pdf Noise-Enhanced Balance Control in Patients with Diabetes and Patients with Stroke.] Ann Neurol 2006;59:4–12. PMID 16287079.</ref>
*[[Stochastic theory of hematopoiesis]]
===Geology===
*[[meander|Stochastic theory of meander formation]]
==Music==
In [[music]], '''stochastic''' elements are randomly generated elements created by strict [[mathematics|mathematical]] processes.
Stochastic processes can be used in music to compose a fixed piece or can be produced in performance. Stochastic music was pioneered by [[Iannis Xenakis]], who used [[probability]], [[game theory]], [[group theory]], [[set theory]], and [[Boolean algebra (logic)|Boolean algebra]], and frequently used [[computer]]s to produce his scores. Earlier, [[John Cage]] and others had composed ''[[aleatoric music|aleatoric]]'' or [[indeterminate music]], which is created by chance processes but does not have the strict mathematical basis (Cage's ''[[Music of Changes]]'', for example, uses a system of charts based on the [[I-Ching]]).
== 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. [[Color printing]] is a binary system, where ink is either present or not present, so all color separations to be printed must be translated into dots at some stage of the workflow. Traditional [[linescreen]]s which are [[amplitude modulation|amplitude modulated]] had problems with [[moiré]] but were used until stochastic screening became available. A stochastic (or [[frequency modulation|frequency modulated]]) dot pattern creates a more photorealistic image.
==Language and linguistics==
Non-deterministic approaches in language studies are largely inspired by the work of [[Ferdinand de Saussure]]. In [[usage-based model|usage-based linguistic theories]], for example, where it is argued that [[competence]], or langue, is based on [[performance]], or [[parole]], in the sense that linguistic knowledge is based on frequency of experience, grammar is often said to be [[probability|probabilistic]] and variable rather than fixed and absolute. This is so, because one's [[competence]] changes in accordance with one's experience with linguistic units. This way, the frequency of [[usage-events]] determines one's knowledge of the language in question. For much later work in this area, see [[Julia Kristeva]] on her usage of the 'semiotic,' [[Luce Irigaray]] on reverse Heideggerian epistomology, and [[Pierre Bourdieu]] on polythetic space for examples of stochastic social science theory.
==Finance==
The financial markets use stochastic models to value options on stock prices, bond prices, and on interest rates, see [[Markov_chain|Markov models]]. Moreover, it is at the heart of the [[Insurance|insurance industry]].
Not to be confused with [[stochastic oscillator]]s in [[Technical Analysis]].
==References==
<references/>
==Further reading==
*''Formalized Music: Thought and Mathematics in Composition'' by [[Iannis Xenakis]], ISBN 1-57647-079-2
*''Frequency and the Emergence of Linguistic Structure'' by Joan Bybee and Paul Hopper (eds.), ISBN 1-58811-028-1/ISBN 90-272-2948-1 (Eur.)
[[Category:Mathematical terminology]]
[[Category:Financial terminology]]
[[Category:Statistical randomness]]
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