stochastic

Adj: random, randomly determined

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The adjective “stochastic” implies the presence of a random variable; e.g. stochastic variation is variation in which at least one of the elements is a variate and a stochastic process is one wherein the system incorporates an element of randomness as opposed to a deterministic system.

—A Dictionary of Statistical Terms, 5th edition, prepared for the International Statistical Institute by F.H.C. Marriott. Published for the International Statistical Institute by Longman Scientific and Technical.

[From Ancient Greek στοχαστικός (stokhastikós), from στοχάζομαι (stokházomai, “aim at a target, guess”), from στόχος(stóhos, “an aim, a guess”).]

In probability theory, a purely stochastic system is one whose state is randomly determined, having a random probability distribution or pattern that may be analyzed statistically but may not be predicted precisely. In this regard, it can be classified as non-deterministic (i.e., “random”) so that the subsequent state of the system is determined probabilistically. Any system or process that must be analyzed using probability theory is at least partly stochastic. Stochastic systems and processes play a fundamental role in mathematical models of phenomena in many fields of science, engineering, finance, and economics.

So then,

A stochastic event or system is one that is unpredictable because of a random variable.

Spinoffs

Mathematics: based on the theory of probability

Artificial intelligence: stochastic neural networks

Natural science

Physics

Stochastic Monte Carlo method

  • Enrico Fermi, in 1930, used a random method to calculate the properties of the newly discovered neutron
  • simulations required for the Manhattan Project
Biology

Stochastic resonance — 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

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[Image: f4.bcbits.com]

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[Image: sine.ni.com]

Medicine

Stochastic effect, or “chance effect” is one classification of radiation effects that refers to the random, statistical nature of the damage.

ijms-15-08169f1-1024

[Image: MDPI]

Geomorphology

Stochastic theory of meander formation

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[Image: Hydrotopics]

Creativity

creativity in science (of scientists) is a constrained stochastic behaviour such that new theories in all sciences are, at least in part, the product of a stochastic process.

Computer Science
  • Stochastic ray tracing is the application of Monte Carlo simulation to the computer graphics ray tracing algorithm.
Music

Stochastic processes may be used in music to compose a fixed piece or may be produced in performance. Stochastic music was pioneered by Iannis Xenakis, who coined the term stochastic music.

Subtractive color reproduction

A stochastic (or frequency modulated) dot pattern creates a sharper image.

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[Image: Pinterest]

Language and Linguistics

Conception of grammar as probabilistic

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For an entire sentence, we generate all of its possible parse trees, and then compute the probability that each of those trees will occur, using the above strategy. The preferred parse tree is the one whose probability is the maximum. [Text and Image: Bowdoin.edu]

Social Sciences

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.

Business

Manufacturing processes, continuous or batch, are assumed to be stochastic processes. The process is monitored using a process control chart which plots a given process control parameter (usually many parameters are tracked simultaneously) over time. Statistical models define limit lines which define when corrective actions must be taken to bring the process back to its intended operational window.

Finance — stochastic oscillator

The financial markets use stochastic models to represent the seemingly random behaviour of assets such as stocks, commodities, relative currency prices (i.e., the price of one currency compared to that of another, such as the price of US Dollar compared to that of the Euro), 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.

Media

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.

Notable uses of the word “stochastic”

Self-slaughter, as Hamlet always says, was certainly in the cards, unless one had been out here long enough to have contemplated the will of God, observed the stochastic whimsy of the day, learned when and when not to whisper Insh’allah,” and understood how, as one perhaps might never have in England, to await, to depend upon, the ineluctable departure of what was most dear.

—2006, Thomas Pynchon, Against the Day, Vintage 2007, p. 854

In the evening, while she bathed, waiting for him to enter the bathroom as she powdered her body, he crouched over the blueprints spread between the sofas in the lounge, calculating a stochastic analysis of the Pentagon car park.

—1970, J. G. Ballard, The Atrocity Exhibition

[Ed: Tis true, I have very little comprehension of the concepts entertained above. But me likes the word, stochastic.]hackles-stochastic

The wind bloweth where it listeth, and thou hearest the sound thereof, but canst not tell whence it cometh, and whither it goeth: so is every one that is born of the Spirit.

Are you of the Spirit? Are you a stochastic system?

References

 

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