(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. Additional examples are warfare, meteorology and rhetoric, where success and failure are difficult enough to predict that explicit allowances are made for uncertainty.
, 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.
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.
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.
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.
elements are randomly generated elements created by strict mathematical
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).
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 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.
The financial markets use stochastic models to represent the seemingly random behaviour of assets such as stocks
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.)