Stochastic (/stəˈkæstɪk/; from Ancient Greek στόχος (stókhos) 'aim, guess')[1] is the property of being well-described by a random probability distribution.
[1] Stochasticity and randomness are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; in everyday conversation, however, these terms are often used interchangeably.
[15][16] It is also used in finance (e.g., stochastic oscillator), due to seemingly random changes in the different markets within the financial sector and in medicine, linguistics, music, media, colour theory, botany, manufacturing and geomorphology.
[20] This phrase was used, with reference to Bernoulli, by Ladislaus Bortkiewicz,[21] who in 1917 wrote in German the word Stochastik with a sense meaning random.
[24] 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.
[25][22][a] Further fundamental work on probability theory and stochastic processes was done by Khinchin as well as other mathematicians such as Andrey Kolmogorov, Joseph Doob, William Feller, Maurice Fréchet, Paul Lévy, Wolfgang Doeblin, and Harald Cramér.
Monte Carlo methods were central to the simulations required for the Manhattan Project, though they were severely limited by the computational tools of the time.
The RAND Corporation and the U.S. Air Force were two of the major organizations responsible for funding and disseminating information on Monte Carlo methods during this time, and they began to find a wide application in many different fields.
"Distributed ray tracing samples the integrand at many randomly chosen points and averages the results to obtain a better approximation.
It is essentially an application of the Monte Carlo method to 3D computer graphics, and for this reason is also called Stochastic ray tracing.
Non-deterministic approaches in language studies are largely inspired by the work of Ferdinand de Saussure, for example, in functionalist linguistic theory, which argues that competence is based on performance.
To the extent that linguistic knowledge is constituted by experience with language, grammar is argued to be probabilistic and variable rather than fixed and absolute.
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[citation needed] and is part of the Cinematic Contagion Systems patented by Geneva Media Holdings, and such modeling has been used in data collection from the time of the original Nielsen ratings to modern studio and television test audiences.
[citation needed] Xenakis frequently used computers to produce his scores, such as the ST series including Morsima-Amorsima and Atrées, and founded CEMAMu.
Modern electronic music production techniques make these processes relatively simple to implement, and many hardware devices such as synthesizers and drum machines incorporate randomization features.
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.