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WikiProject Mathematics (Rated B-class, Mid-importance)
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This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
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 Field: Probability and statistics
One of the 500 most frequently viewed mathematics articles.

References needed[edit]

The only reference cited to Iannis Xenakis as being the pioneer in stochastic music generation is a book by himself and a link to his Wikipedia page. Unless a third-party reference can be cited, the information should be deleted, according to the Wikipedia Verifiability policy (Wikipedia:Verifiability) --Armando Serrano 16:33, 4 December 2006 (UTC)


Stochastic means unknowable not random.

If say we have an asteroid, then its 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, its movments are not random but stochastic.

The decay of an atomic nucleus is random according to modern physics.

I think this is correct at least in physics and maths.

--Jirate 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. Michael Hardy 21:31, 6 Sep 2004 (UTC)

- stochastic comes from the Greek "stochastikos" (the Greek on the main page is even in modern Greek). This means 'aiming at a target' as in a target for archers. The word for target is stochos. This implies some level of 'guess'. It has nothing to do with the word 'random'.

So? Etymology is not the same as meaning. That Merriam-webster entry starts "1:RANDOM." Qwfp (talk) 14:59, 10 February 2011 (UTC)

This is one of the few times , in my limited experience, that etymology turns out to be damn near enlightening! Once it is pointed out that a stochos was a stick -- a pointed stick that a Greek archer stuck in the hillside and took shots at with his bow and arrows --- the whole thing starts to make a lot more sense, how it went from the stick; to the pattern of the arrows stuck around the stick; to measurements of the distances from the stick to the arrow holes; and finally to some brilliant Greek like Archimedes or whoever figuring out that Eureka! there's a Pattern! And then the word itself --- stochos -- came to mean target and similarly, "guess". Any time you guess, you're going to guess within an expected range. Funny how all the learned people --- eg people who know Greek, and no doubt Latin too --- don't usually know the yarn about the stick and the archers, and thus don't get the essential IMHO point that it's a real world thing that we're talking about here with the stochos and the stochastic and the stochasticity, where arrows in the real world behave very much like arrows generated by a Macintosh or a Toshiba -- computers who are masters of randomness -- but no computer could ever come up with the outliers you see every great once in a whle at the archery range. Stochastic processes, like the exemplary archery practice, are not Mickey Mouse; they are real.

And thus did we all get to enjoy the benefits of Probability and Statistics, including the wonders of Randomness and Standard Deviation from the Norm. All because of Greek archers just sticking a stick in the hillside, nothing fancy, no bullseye needed, just a stick. Tibetan archers, by the way, use a bone.

I would LOVE to have somebody ring in here who actually is a native Greek speaker and grew up with the culture enough to comment on the words being bandied about here. I'm going out on a limb myself, because I looked up stochos , in Greek, in a three inch thick Greek-English lexicon, and it only had "target" and "guess", with lots of scholarship attached, and no mention of sticks. Maybe somebody along the line got fooled by how stochos and stick sound and look a lot alike. In Greek, that middle letter is a chi, not a kappa, which to me seems like a dead giveaway; but I'd love to hear from a Greek scholar here. Richard8081 (talk) 21:14, 22 January 2013 (UTC)


>by either the previous state of the environment.

Shouldn't there be an "or" phrase to explain the "either"?

-I think it means "by either the previous state or the environment". If this is wrong, plrease revert-Akshayaj 18:45, 19 July 2006 (UTC)

Color Reproduction and Stochastic screening[edit]

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. Traditionallinescreens (amplitude modulated) had been used up until stochastic screening became available. A stochastic (or frequency modulated) dot pattern creates a more photorealistic image. --Dkroll2 16:27, Dec 27, 2004 (UTC)


I dont know about the past, but currently, is this article a disambiguation page? Form a rough scan of it, it seems to be an encyclopedia article, and not a disabiguation. If I am wrong, by all means, please explain. Otherwise, I make a motion to remove the disambiguation label at teh bottom.--Vox Causa 15:47, 26 September 2006 (UTC)

Second. This page is showing up at Wikipedia:Disambiguation pages with links, but it would not be possible to follow the normal procedure (see that page) by changing links to this page to link directly to the appropriate articles; it's not clear, from this page, what one would link to in each case. For an example of a page that *does* offer pages to link to when cleaning up such links (a page I happen to have adopted), see Swedish. --Tkynerd 01:21, 9 October 2006 (UTC)
I have proposed this page to be split. Read more under Proposed Split below. HymylyT@C 20:46, 2 February 2007 (UTC)

Stochastic roots[edit]

Stochastic word comes from ancient Greek word "stochasticos" [adjective], meaning to aim to achieve a goal, but also meaning "assumed", "supposed", "hypothetical". "Stochasticos" is used nowadays in Greek literature and technical books. The word "stochastikos" comes from "stochazomae" meaning to make assumtions-hypothesis, to think. The root word for all the words (stochastikos,stochazomae) is the word "stochos" which means "aim","goal".

It is used to give a property to a person or an object.

ex.'This algorithm uses stochastic procedure' meaning that the algorithm makes its own hypothesis; that the code is not determenistic.

Stochastic vs Non-deterministic[edit]

I think there is a difference between 'Stochastic' and 'Non-deterministic'. I read something about a 'Stochastic and Non-deterministic' calculus and a 'Stochastic and Deterministic' calculus. --hzmonte 27 January 2007

Actually, everything is stochastic that has an uncountable measure because of Heisenburg's Uncertainty Principle, i.e. everything is unknowable if its measurement is a continuum, because it cannot be known precisely. However, it can be assigned a probability distribution, which itself is unknowable and hence stochastic. Localchurch (talk) 17:53, 27 March 2009 (UTC)

Proposed Split[edit]

I have proposed this page to be split. It is not structured like a proper encyclopaedic article, and there is enough to be said about each of the subtopics to form complete articles on them. My vision is that this be turned into a redirect to Stochastic process or similar. Please leave your comments. HymylyT@C 20:46, 2 February 2007 (UTC)

I agree it should be split up. This article may become a disambiguation page rather than a redirect, eg. stochastic event, stochastic process, etc. But yes, articles should be about nouns, not adjectives. And splitting the article makes sense regardless. —Pengo 22:49, 2 February 2007 (UTC)
Does someone just split the page up themselves or do people just leave it for Admins to take care of? --Huper Phuff talk 21:20, 12 July 2007 (UTC)
Agree with the split. (Which is something users does by themselves, rather than admins.) —Quasirandom 18:31, 29 July 2007 (UTC)
Can I disagree for now but think it's eventually a good idea? Right now, it's really great to have all the topics together, and because they are pretty much just a blurb, it's readable and concise. Yet, each section doesn't seem to merit a page on their own--yet technically they should be their own page. But Wikipedia, I've noticed, doesn't operate on technicalities, it operates on what the wikipedia people think, according to the wikipedia principles of course. So, according to this, I'd use the notability thing which says that the article should be notable. Right now, it seems like the sections aren't notable enough to merit their own section (no section has more than 5 sentances); if the sections become more notable, then I say split it up! Rhetth (talk) 02:56, 12 December 2007 (UTC)


Stochastic. I'm not sure how the splits are formed, but I am thinking that one can talk about Stochastic philosophy, stochastics in psychology (e.g. stochastic optimal feedback control model) and in mathematics.
Split, folks, split. The sooner the better. Having small sections in a big article discourages section improvement. The new articles can be stubs, but my guess is, they probably will not remain stubs long. As far as having it all together is concerned, that is what the disambig aspect is for. Instead of having a disambig however I would suggest judicious use of "main" and "details". That way it is easy for anyone just to start a stub containing the bulk of the section and reduce the section in this article to a one- or two-liner introduced by a "main."Dave (talk) 14:44, 14 February 2008 (UTC)
2 more cents from me: As the article topics get made into seperate main articles, should this page even exist? I think so, because no one article should give the full breadth and explaination of the general idea of what is stochastic. Stochastic has been used to refer to many different ideas, and this article should be the melting pot for them all, vs. each single stochastic article representing its perspective.

Regardless of whether there is a split or not, I think there needs to be clear distinction between at least the following: 1. The definition and theory of stochastic processes, which at a glance seems to be well covered in the article Stochastic process; 2. Examples of real world processes observed to have stochasitc characteristics, which this article contains some examples of. 3. Application of stochastic methods to solve problems, learn more about the world, or create things; this article touches on some examples, but also the articles Monte_Carlo_method, Stochastic_simulation, Gillespie_algorithm, Stochastic_optimization, and several more, are very relevant. —Preceding unsigned comment added by Sscomp2004 (talkcontribs) 10:03, 22 November 2009 (UTC)

Split, and merge relevant bits into Stochastic process. Wikiphile1603 (talk) 18:19, 4 February 2010 (UTC)

stochastic events in biology[edit]

there should be something mentioned about stochastic events in developmental biology. this is about the random chances or unseen factors that affect the phenotype of organisms with the same genotype in the same environment.... 00:44, 17 May 2007 (UTC)

Poor Examples[edit]

I don't think the classic examples given for stochastic processes do a good job of illustrating what a stochastic process is. At least, I don't think the connection is explained well. The way it's written, stochastic processes are all about the unpredictability of success given a certain input. Worse, one might come away thinking a stochastic process is defined as one in which one does not obtain optimal benefit.

Rather in doctoring, it might better be stated that not all patients with equivalent symptoms will necessarily react the same way to a given treatment, or in war, that a given strategy countered against another will not always result in the same level of success, neither can outcomes be certainly predicted by the relative strengths of the armies involved.

I'm going to make some changes along these lines.--Seanmcox (talk) 20:26, 16 January 2008 (UTC)

Yes, the given examples totally suck. Following their (absurd) form, I could just as well say that adding two numbers is a stochastic process, because knowing their signs is not sufficient to determine their sum. That is, applying the same addition-treatment to several number-patients exhibiting the same sign-symptoms doesn't mean their sum-reactions will be the same. Further, the examples cite a philosophical paper. While this source helps to make clear the etymology of the term, it has no practical bearing, whatsoever, on the conceptual formulation of this inherently mathematical idea. So, yeah, get rid of it; SECONDED. —Preceding unsigned comment added by (talk) 23:13, 12 February 2008 (UTC)
Hmmm... some interesting ideas. But,, it doesn't look good to start a discussion with 'absurd' and 'totally suck' & not even sign in. Someone might think you just like to talk but not follow up on your statements. As far as the number-crunching counter-example goes, you are right. So far, only first order arithmetic has been found to be consistent and complete. For addition, a guy named Goedel came up with some hair-brained idea that it, along with other basic arithmetical truths, are founded on logic which proves itself true, which of course makes it inconsistent.
As far as the source goes, it gives a definition of non-mathematical stochastic processes, so why do you say that stochastic things are inherently mathematical? "Stochastic crafts are those, like rhetoric and medicine, in which the achievement of the stated aim of the craft can and must be distinguished from the question whether the craft is being practiced perfectly." I can get you a full copy of the paper if you like.
As far as the examples given, and the new wording, I would say they are technically correct, but perhaps we could include examples for the mathematical stochastic processes and for non-mathematical stochastic processes ("stochastic crafts" per the source)? I think that would give both ideas more dignity and clairity. Also, the rewording of the medical example ("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") is technically correct, but as the source talks about the perfect doctoring ("So even if the doctor's patient dies, he may have practiced his craft [perfectly]...") it seems to be talking about the practice of the craft, not the performance of the pill. The medicine itself (the pill, knowledge) can be treated like a function or an algorithm, but the practice of medicine cannot. Even if the doctor does everything 'correct' during treatment, she may still fail to cure the patient. So I think the example for medicine should include something referring to the process of determining a treatment vs. the treatment itself. Rhetth (talk) 01:08, 17 March 2008 (UTC)
You are correct that it is poor form to not sign one's post. (Though, I will point out that you do the same on the comment you left on my user page's discussion page. :-D) Our anonymous friend is also, I think, a little "absurd", if you will, but for the same reason, I think your own classifications a bit specious. (But not wholly without merit.) Mathematics is all about using numbers to describe real world phenomena. A large majority, I would think, of mathematicians would tell you that there is no such thing as non-mathematical phenomena. (Though this is a more generally philosophical point.) What our anonymous friend fails to realize, among other things, is that I do not criticize the source or the context of the examples (for such is comparatively irrelevant), but I rather criticized the uniformity with which they characterized Stochastic processes by a tendency towards failure despite some "perfect" strategy (or input) being employed. That is only one of many consequences of some stochastic processes, but not by any means a defining characteristic.
I will also point out to our anonymous friend that mathematics cannot by any means be separated from philosophy. In fact, mathematics was born of philosophy. (If I recall correctly, Goedel, before coming to the United States, worked in the philosophy department. "Logic" was not really considered worthy of the mathematics department at that time, odd though that idea may sound.) Philosophy, like mathematics, is all about gaining understanding and approaching truth. Science and Mathematics are both products of philosophy; tools developed and refined by philosophers to accomplish this end. It should not be either surprising or distasteful to us to find philosophy blended with our mathematics. Further, there is a curious idea held by many mathematicians, and non-mathematicians, that the conclusions of mathematics are unassailable. Goedel "proved" this assumption wrong, somewhat quixotically, but still it persists. (Not that we don't have particularly strong reasons to place our confidence in mathematics.)
--Seanmcox (talk) 17:23, 23 September 2008 (UTC)


I'm really not sure Cancer is a good example of stochastic effects in medicine. I believe cancer as an outcome of radiation exposure may well be but surely there are too many enviromental and biological influences on cancer development for it to be stochastic. Lady of the dead (talk) 16:42, 10 August 2009 (UTC)


I would really suggest an inclusion about the use of stochastic physics processes in climate modelling, including seasonal to decadal to centennial timescales.

Weatherlands (talk) 09:39, 24 March 2011 (UTC)

Stochastic Terrorism[edit]

Must read articles: and*Pictures-fixed*- . Maybe the wikipedia article could include something about stochastic Terrorism, taking examples from the linked articles.... AugustinMa (talk) 13:36, 28 July 2011 (UTC)

Doubly Stochastic[edit]

I am running into the term Doubly Stochastic and would like to know what this term means? See D. Lando and M. S. Nielsen 2010, J. of Financial Intermediation (Elsevier) 19: 344-372. — Preceding unsigned comment added by (talk) 14:10, 28 March 2012 (UTC)

on language[edit]

The following quote is based on a fundamental misunderstanding:

"...In usage-based linguistic theories, for example, where it is argued that competence, or langue, is based on performance, or parole,..."

Chomsky's 'competence' is a mentalistic notion - an individual's knowledge of language - 'performance' is everything else and is not necessarily indicative of 'competence'.

Saussure's 'langue' is a social notion - a snap-shot of the abstract system of language as it exists at a given point in time - a system which is shared among a community and is not the property of any single speaker. 'Parole' is language in use, and is the 'actual' from which 'langue' is abstracted.

Equating Chomsky's notions and Saussure's notions is a fundamental misunderstanding of one, or both. Chomsky's theory of language is NOT a 'useage-based' theory, and the fundamental conceptualisations of what language actually _is_ in Chomsky's theory on one hand, and theories which take language use into account on the other, are not even the same thing.

See (for example):

Chomsky, N. (1965). Aspects of the theory of syntax. Cambridge, Massachusetts: Massachusetts Institute of Technology. pp. 3ff.

de Saussure, F. (1983). Course in general linguistics (R. Harris, Trans.). London: Duckworth. pp. 13ff. (talk) 08:17, 24 April 2012 (UTC)

Modeling: Markov chain Monte Carlo (MCMC)[edit]

See: Markov chain Monte Carlo — Preceding unsigned comment added by Jim.Callahan,Orlando (talkcontribs) 21:01, 21 March 2013 (UTC)

Modeling: Agent-based model[edit]

See: Agent-based model Jim.Callahan,Orlando (talk) 21:03, 21 March 2013 (UTC)

Should Artificial Intelligence be a subtopic under computer science?[edit]

Jim.Callahan,Orlando (talk) 21:06, 21 March 2013 (UTC)

Assessment comment[edit]

The comment(s) below were originally left at Talk:Stochastic/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

This article should probably be in several other WikiProjects too. Personally I'm not too keen on splitting it as all the fields use "stochastic" to mean essentially the same thing. It gets quite a lot of views but I'd conjecture that most people are after little more than a dictionary definition. It's interesting and probably of some use to see what fields use it and in what context and give some links. Perhaps that's really enough? Qwfp (talk) 15:16, 22 February 2008 (UTC)

Last edited at 15:16, 22 February 2008 (UTC). Substituted at 20:15, 1 May 2016 (UTC)

Stochastic Terrorism[edit]

Might Wikipedians add a section on "Stochastic Terrorism" as that word is being used to analyze and explain Donald J. Trump's odd remarks about 2nd Amendment People doing something about Hillary R. Clinton... It would be appreciated. Emyth (talk) 23:27, 10 August 2016 (UTC)

I'm trying to figure out whether the term "Stochastic Terrorism" is well-documented enough, and furthermore whether other names have been suggested to define the same thing. I'll be working on this over the next days and weeks. So far the only source I can find is which, though hosted on a blogging service, consists simply of one entry defining, possibly coining, the term in extreme detail via essay. I could use help on this, contact me via User_talk:Harlequence or in this subsection if you have more sources, information, or general desire to contribute. Harlequence (talk) 19:32, 11 August 2016 (UTC)
Alas, this may be too early in the nascence of the use of this term...and thus go against the Wikipedian ethos of mere description of knowledge... That would be a shame... I, as a professor of Literacy at a public university need references to the concept and responsible discussion of the term...particularly if it is New and being found Useful... I will try to collect the Mainstream Media references...(in all my spare time one week before a new semester!) Thank you for listening and considering my request. All the best! Emyth (talk) 12:35, 12 August 2016 (UTC)

broken PDF link[edit]

this is broken

"Noise-Enhanced Balance Control in Patients with Diabetes and Patients with Stroke" (PDF)  — Preceding unsigned comment added by (talk) 12:55, 27 December 2016 (UTC)