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# Stochastic

"Stochastic" (from the Greek "Στόχος" for "aim" or "guess") means random.

A stochastic process is one whose behavior is non-deterministic in that a state's next state is determined both by the process's predictable actions and by a random element. Stochastic crafts are complex systems whose practitioners, even if complete experts, acknowledge that outcomes result from both known and unknown causes. 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. [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] Additional examples are warfare, meteorology and rhetoric, where success and failure are difficult enough to predict that explicit allowances are made for uncertainty.

Mathematical theory

In mathematics, specifically in probability theory, the field of stochastic processes 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 that has non-negative 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 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 properties of the system.

Biology

*Stochastic resonanceIn 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. [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.]

*Stochastic theory of hematopoiesis

Geology

Music

In music, stochastic elements are randomly generated elements created by strict 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, and frequently used computers to produce his scores. Earlier, John Cage and others had composed "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 linescreens which are amplitude modulated had problems with moiré but were used until stochastic screening became available. A stochastic (or 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 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 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.

Manufacturing

Manufacturing processes are assumed to be stochastic processes. This assumption is largely valid for either continuous or batch manufacturing processes. Testing and monitoring of the process is recorded using a process control chart which plots a given process control parameter over time. Typically a dozen or many more parameters will be tracked simultaneously. Statistical models are used to define limit lines which define when corrective actions must be taken to bring the process back to its intended operational window.

Finance

The financial markets use stochastic models to represent the seemingly random behaviour of assets such as stocks, commodities and interest rates. These models are then used by quantitative analysts to value options on stock prices, bond prices, and on interest rates, see Markov models. Moreover, it is at the heart of the insurance industry.

Not to be confused with stochastic oscillators in Technical Analysis.

*"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.)

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### Look at other dictionaries:

• Stochastic — Sto*chas tic (st[ o]*k[a^]s t[i^]k), a. [Gr. stochastiko s, from stocha zesqai to aim, to guess, fr. sto chos mark or aim.] 1. Conjectural; able to conjecture. [Obs.] Whitefoot. [1913 Webster] 2. random; chance; involving probability; opposite of …   The Collaborative International Dictionary of English

• stochastic — 1660s, pertaining to conjecture, from Gk. stokhastikos able to guess, conjecturing, from stokhazesthai guess, from stokhos a guess, aim, target, mark, lit. pointed stick set up for archers to shoot at (see STING (Cf. sting)). The sense of… …   Etymology dictionary

• stochastic — [stō kas′tik, stəkas′tik] adj. [< Gr stochastikos, proceeding by guesswork, lit., skillful in aiming < stochazesthai, to aim at < stochos, a target: for IE base see STING] 1. of, pertaining to, or arising from chance; involving… …   English World dictionary

• stochastic — adjective Etymology: Greek stochastikos skillful in aiming, from stochazesthai to aim at, guess at, from stochos target, aim, guess more at sting Date: 1934 1. random; specifically involving a random variable < a stochastic process > 2. involving …   New Collegiate Dictionary

• Stochastic — Стохастический индикатор (англ. stochastic oscillator) индикатор технического анализа, который показывает положение текущей цены относительно диапазона цен за определенный период в прошлом. Стохастика измеряется в процентах; значение выше 80%… …   Википедия

• stochastic — sto·chas·tic stə kas tik, stō adj 1) involving a random variable <a stochastic process> 2) involving chance or probability <a stochastic model of radiation induced mutation> sto·chas·ti·cal·ly ti k(ə )lē adv * * * sto·chas·tic (sto… …   Medical dictionary

• stochastic — having components affected by random variability, e.g. future recruitments in a fishery are projected with a stochastic component (random variables) to allow for unexplained effects …   Dictionary of ichthyology

• stochastic — adjective /stəˈkæstɪk/ Random, randomly determined. In the evening, while she bathed, waiting for him to enter the bathroom as she powdered her body, he crouched over the blueprints spread between the sofas in the lounge, calculating a stochastic …   Wiktionary

• stochastic — A term used to describe outcomes based on uncertain relationships. The process of change in a variable resulting from change in a parameter. For example, option adjusted spread measures of yield and Monte Carlo models of interest rate risk are… …   Financial and business terms

• stochastic — tikimybinis statusas T sritis automatika atitikmenys: angl. stochastic vok. stochastisch rus. стохастический pranc. stochastique ryšiai: sinonimas – stochastinis …   Automatikos terminų žodynas