Stochastic
Stochastic, from the Greek "stochos" or "goal", means random. A stochastic process is one whose behavior is non-deterministic in that the next state of the environment is not fully determined by the previous state of the environment.
Mathematical theory
In mathematics, specifically in probability theory, the field of stochastic processes has for some decades been a major area of research, to which hundreds of researchers have devoted their careers. See that article for more.
Artificial intelligence
In artificial intelligence stochastic programs work by using probabilistic methods to generate emergent properties, that is, characteristics that were not explicitly programmed in. 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. Even though each molecule is moving deterministically, a collection of them is unpredictable (this is an example of chaos out of order). 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.
Music
In music stochastic elements are randomly generated elements created by strict mathematical processes.
Stochastic processes can be used in music either to compose a fixed piece, or 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 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).
Further reading
- Formalized Music: Thought and Mathematics in Composition by Iannis Xenakis, ISBN 1576470792
