Stochastic Guide, Meaning , Facts, Information and Description
Stochastic, from the Greek "stochos" or "goal", means of, relating to, or characterized by conjecture; conjectural; 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.
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.
A stochastic matrix is a matrix that has non-negative real entries that sum to 1 in each column.
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.
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.
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).
In the visual arts, Yoshiyuki Abe[1], has mastered the art of creation through stochastic process. His work uses geometric objects, mostly the surfaces of hyperbolic paraboloids, and the processing of stochastic elements. In his words: "No matter how you use a computer, or whichever computer you use, to create an art work is not easy. Nevertheless, I believe artists can find a new horizon in his/her creative activities by having the experience of using geometric object and/or stochastic process. For artists who want to create mathematical art through algorithm-driven parameter control, the essential element for success is artistic serendipity. This is the interesting fact of art in the perfect mathematical space." - Y. AbeMathematical theory
Artificial intelligence
Natural science
Music
Visual Arts