''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. ==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. A stochastic matrix is a matrix (mathematics) that has non-negative real number entries that sum to 1 in each column. ==Artificial intelligence== In artificial intelligence stochastic programs work by using probabilistic methods to solve problems, as in simulated annealing, Stochastic neural network 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. Even though each molecule is moving deterministically, a collection of them is unpredictable (this is an example of chaos arising from 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 property of the system. ==Music== In music stochastic elements are randomly generated elements created by strict mathematics 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'' 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). ==Visual arts== In the visual arts, Yoshiyuki Abe[http://www.pli.jp], 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." == Color reproduction == When #color printings are made, the image is separated into its component colors through. 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 modulation had problems with moire but were used until stochastic screening became available. A stochastic (or frequency modulated) dot pattern creates a more photorealistic image. ==Language and linguistics== In usage-based model, 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 probabilism and variable rather than fixed and absolute. This is so, because one's competence changes in accordance with ones experience with linguistic units. This way, the frequency of usage-events determines one's knowledge of the language in question. ==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 902722943/ISBN 9027229481 (Eur.)
Stochastic means unknowable not random. If say we have an asteroid, then it's movments in orbits, over a long period is stochastic. At a fundemental level we cannot measure the position of the asteroid well enough to make acurate long term predictions, however the asteroid was always going to go where it has gone, it's movments are not random but stochastic. The decay of an atomic nucleus is random according to modern physics. I think this is correct atleast in physics and maths. --User:Irate 19:59, 4 Sep 2004 (UTC) :In mathematics it's usually taken to be synonymous with ''random''. But the phrase ''random variable'' is used far more often than ''stochastic variable'' and ''stochastic process'' is used more often than ''random process''. There is also the related question of whether probabilities should be assigned only to things that are random, according to their relative frequencies of occurrence, or to things that are uncertain according to how strongly the evidence supports them. This is central to the Bayesian-versus-frequentist controversy in statistical inference. User:Michael Hardy 21:31, 6 Sep 2004 (UTC) == either...? == >by either the previous state of the environment. Shouldn't there be an "or" phrase to explain the "either"? == Color Reproduction and Stochastic screening == We like to call it "Sarcastic screaming" Is this ok? When color reproductions are made, the image is separaed into it's component colors (color separated through RGB filters). One represents the cyan, magenta, yellow, and black data. Color printing is a binary system, therefore all color films or plates, etc. eventually have to be translated into dots of some sort. Traditional linescreens (amplitude modulated) had been used up until stochastic screening became available. A stochastic (or frequency modulated) dot pattern creates a more photorealistic image. --User:Dkroll2 16:27, Dec 27, 2004 (UTC)
Thanks for the welcome and the helpful links. sorry, forgot to sign User:Stochastic 23:19, 30 Nov 2004 (UTC)
== My Interests == Altaic languages Austria-Hungary India Indo-Iranian languages Iran Levy processes option financial mathematics stochastic process == Changes to Articles == Carl Friedrich Gauss Leonhard Euler Poisson process SAVAK == New Articles == Hassan Pakravan Nasser Moghadam Teymur Bakhtiar
See other meanings of words starting from letter:
Words begining with Stochastic:
Stochastic
Stochastic
Stochastic
Stochastic
Stochastical
Stochastically_independent
Stochastics
Stochastic_Calculus
Stochastic_calculus
Stochastic_context-free_grammar
Stochastic_copula
Stochastic_differential_equation
Stochastic_differential_equation
Stochastic_electrodynamics
Stochastic_gradient_descent
Stochastic_independence
Stochastic_kernel
Stochastic_matrix
Stochastic_matrix
Stochastic_music
Stochastic_neural_network
Stochastic_process
Stochastic_process
Stochastic_processes
Stochastic_processes
Stochastic_processes
Stochastic_process_algebra
Stochastic_programming
Stochastic_programming
Stochastic_ray_tracing
Stochastic_resonance
Stochastic_transition_function
Stochastic_tunneling
Stochastic_tunneling
Stochastic_vacuum_model
Stochastic
''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. ==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. A stochastic matrix is a matrix (mathematics) that has non-negative real number entries that sum to 1 in each column. ==Artificial intelligence== In artificial intelligence stochastic programs work by using probabilistic methods to solve problems, as in simulated annealing, Stochastic neural network 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. Even though each molecule is moving deterministically, a collection of them is unpredictable (this is an example of chaos arising from 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 property of the system. ==Music== In music stochastic elements are randomly generated elements created by strict mathematics 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'' 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). ==Visual arts== In the visual arts, Yoshiyuki Abe[http://www.pli.jp], 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." == Color reproduction == When #color printings are made, the image is separated into its component colors through. 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 modulation had problems with moire but were used until stochastic screening became available. A stochastic (or frequency modulated) dot pattern creates a more photorealistic image. ==Language and linguistics== In usage-based model, 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 probabilism and variable rather than fixed and absolute. This is so, because one's competence changes in accordance with ones experience with linguistic units. This way, the frequency of usage-events determines one's knowledge of the language in question. ==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 902722943/ISBN 9027229481 (Eur.)
Stochastic
Stochastic means unknowable not random. If say we have an asteroid, then it's movments in orbits, over a long period is stochastic. At a fundemental level we cannot measure the position of the asteroid well enough to make acurate long term predictions, however the asteroid was always going to go where it has gone, it's movments are not random but stochastic. The decay of an atomic nucleus is random according to modern physics. I think this is correct atleast in physics and maths. --User:Irate 19:59, 4 Sep 2004 (UTC) :In mathematics it's usually taken to be synonymous with ''random''. But the phrase ''random variable'' is used far more often than ''stochastic variable'' and ''stochastic process'' is used more often than ''random process''. There is also the related question of whether probabilities should be assigned only to things that are random, according to their relative frequencies of occurrence, or to things that are uncertain according to how strongly the evidence supports them. This is central to the Bayesian-versus-frequentist controversy in statistical inference. User:Michael Hardy 21:31, 6 Sep 2004 (UTC) == either...? == >by either the previous state of the environment. Shouldn't there be an "or" phrase to explain the "either"? == Color Reproduction and Stochastic screening == We like to call it "Sarcastic screaming" Is this ok? When color reproductions are made, the image is separaed into it's component colors (color separated through RGB filters). One represents the cyan, magenta, yellow, and black data. Color printing is a binary system, therefore all color films or plates, etc. eventually have to be translated into dots of some sort. Traditional linescreens (amplitude modulated) had been used up until stochastic screening became available. A stochastic (or frequency modulated) dot pattern creates a more photorealistic image. --User:Dkroll2 16:27, Dec 27, 2004 (UTC)
Stochastic
Thanks for the welcome and the helpful links. sorry, forgot to sign User:Stochastic 23:19, 30 Nov 2004 (UTC)
Stochastic
== My Interests == Altaic languages Austria-Hungary India Indo-Iranian languages Iran Levy processes option financial mathematics stochastic process == Changes to Articles == Carl Friedrich Gauss Leonhard Euler Poisson process SAVAK == New Articles == Hassan Pakravan Nasser Moghadam Teymur Bakhtiar
See other meanings of words starting from letter:
S
SB | SC | SD | SE | SF | SG | SH | SI | SJ | SK | SL | SM | SN | SO | SP | SR | SS | ST | SU | SW | SX | SY | SZ |Words begining with Stochastic:
Stochastic
Stochastic
Stochastic
Stochastic
Stochastical
Stochastically_independent
Stochastics
Stochastic_Calculus
Stochastic_calculus
Stochastic_context-free_grammar
Stochastic_copula
Stochastic_differential_equation
Stochastic_differential_equation
Stochastic_electrodynamics
Stochastic_gradient_descent
Stochastic_independence
Stochastic_kernel
Stochastic_matrix
Stochastic_matrix
Stochastic_music
Stochastic_neural_network
Stochastic_process
Stochastic_process
Stochastic_processes
Stochastic_processes
Stochastic_processes
Stochastic_process_algebra
Stochastic_programming
Stochastic_programming
Stochastic_ray_tracing
Stochastic_resonance
Stochastic_transition_function
Stochastic_tunneling
Stochastic_tunneling
Stochastic_vacuum_model
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