Dictionary Definition
stochastic adj : being or having a random
variable; "a stochastic variable"; "stochastic processes"
User Contributed Dictionary
English
Etymology
From , from ‘aim at a target, guess’, from ‘an aim, a guess’.Pronunciation
 /stəˈkæstɪk/

 Rhymes: æstɪk
Adjective
 Random,
randomlydetermined.
 1970, J. G.
Ballard, The Atrocity Exhibition:
 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 analysis of the Pentagon car park.
 2006, Thomas Pynchon, Against the Day, Vintage 2007, p. 854:
 Selfslaughter, as Hamlet always says, was certainly in the cards, unless one had been out here long enough to have contemplated the will of God, observed the stochastic whimsy of the day, learned when and when not to whisper “Insh'allah,” and understood how, as one perhaps might never have in England, to await, to depend upon, the ineluctable departure of what was most dear.
 1970, J. G.
Ballard, The Atrocity Exhibition:
Translations
 Danish: stokastisk
 Finnish: stokastinen
 French: stochastique
 German: stochastisch
 Romanian: stocastic
 Spanish: estocástico
 Swedish: stokastisk
Derived terms
Extensive Definition
Stochastic, from the Greek
"Στόχος" which means "aim, guess", means of, relating to, or
characterized by conjecture and randomness.
A stochastic
process is one whose behavior is nondeterministic 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.
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 processes has for some decades been a major area of research. It is commonly assumed to be related to statistics, this is in fact wrong as stochastics are often used in physical systems. So studying stochastics is not the same as studying statistics.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
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.
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
IChing).
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
Nondeterministic approaches in language studies are largely inspired by the work of Ferdinand de Saussure. In usagebased 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 usageevents 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 models. Moreover, it is at the heart of the insurance industry.Not to be confused with stochastic
oscillators in Technical
Analysis.
References
Further reading
 Formalized Music: Thought and Mathematics in Composition by Iannis Xenakis, ISBN 1576470792
 Frequency and the Emergence of Linguistic Structure by Joan Bybee and Paul Hopper (eds.), ISBN 1588110281/ISBN 9027229481 (Eur.)
stochastic in Arabic: عشوائي
stochastic in German: Stochastik
stochastic in Spanish: Estocástico
stochastic in Galician: Estocástico
stochastic in Croatian: Stohastika
stochastic in Japanese: 確率論的
stochastic in Norwegian: Sannsynlighet
stochastic in Portuguese: Estocástico
stochastic in Russian:
Стохастический
Synonyms, Antonyms and Related Words
aimless, aleatoric, aleatory, amorphous, blobby, blurred, blurry, broad, casual, causeless, chance, chancy, chaotic, confused, designless, disordered, driftless, dysteleological,
foggy, fuzzy, general, haphazard, hazy, hitormiss, illdefined,
imprecise, inaccurate, inchoate, incoherent, indecisive, indefinable, indefinite, indeterminable, indeterminate, indiscriminate, indistinct, inexact, inexplicable, lax, loose, mindless, nonspecific, obscure, orderless, promiscuous, purposeless, random, shadowed forth, shadowy, shapeless, stray, sweeping, unaccountable, unclear, undefined, undestined, undetermined, undirected, unmotivated, unplain, unspecified, vague, veiled