Wikipedia:WikiProject Mathematics/PlanetMath Exchange/60-XX Probability theory and stochastic processes

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This page provides a list of all articles available at PlanetMath in the following topic:

60-XX Probability theory and stochastic processes.

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Status means PM article
N not needed
A adequately covered
C copied
M merged
NC needs copying
NM needs merging
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60-00 General reference works (handbooks, dictionaries, bibliographies, etc.)[edit]

Ben Cairns 12:47, 1 Feb 2005 (UTC).
AdamSmithee 15:43, 4 January 2006 (UTC)[reply]
AdamSmithee 15:43, 4 January 2006 (UTC)[reply]
AdamSmithee 15:43, 4 January 2006 (UTC)[reply]
... but could use some clean-up. Ben Cairns 05:57, 2 Feb 2005 (UTC).
Some minor deficiencies in the WP article were rectified, and the article refactored. Added reference to PM article. Ben Cairns 03:44, 2 Feb 2005 (UTC).
AdamSmithee 17:35, 4 January 2006 (UTC)[reply]
Moment generating function.Also the WP article could use a Probability distribution infobox AdamSmithee 17:35, 4 January 2006 (UTC)[reply]
Done AdamSmithee 08:37, 19 April 2006 (UTC)[reply]
Expanded on the WP article, removing an old stub notice in the process. PM article has a nice stochastic process example (interarrival times of a Poisson process), but it didn't seem necessary to add it in. Ben Cairns 05:55, 2 Feb 2005 (UTC).
WP articles contain all the same information and more, but could use some work. Ben Cairns 00:48, 3 Feb 2005 (UTC).
PM article more directly general, but the WP article is easier to understand and is extended to the general case. Ben Cairns 12:45, 1 Feb 2005 (UTC).
Merged in a little definitional stuff. The WP article still needs a bit of work, including possible merging with WP articles on continuous random variables and discrete random variables. Ben Cairns 04:04, 3 Feb 2005 (UTC).
AdamSmithee 17:35, 4 January 2006 (UTC)[reply]
AdamSmithee 17:35, 4 January 2006 (UTC)[reply]
... but only by a sentence or two. Ben Cairns 02:35, 4 Feb 2005 (UTC).
List of textbooks AdamSmithee 14:07, 6 March 2006 (UTC)[reply]

60A05 Axioms; other general questions[edit]

Ben Cairns 05:40, 3 Feb 2005 (UTC).
Made a couple of minor corrections and a small addition. Ben Cairns 05:40, 3 Feb 2005 (UTC).
Ben Cairns 05:42, 3 Feb 2005 (UTC).

60A10 Probabilistic measure theory[edit]

Tricky one. PM article covers both almost surely and almost everywhere, but seems more about the former. Special case of PM's example appears in WP's almost everywhere (along with other examples given in some complicated inline maths). PS: I've fixed the inline unpleasantness. Ben Cairns 13:09, 1 Feb 2005 (UTC).
AdamSmithee 17:38, 4 January 2006 (UTC)[reply]
WP article includes joint probability mass functions. Ben Cairns 01:46, 16 Feb 2005 (UTC).
Or just the information about distribution functions added without copying (it isn't much, really). Ben Cairns 01:46, 16 Feb 2005 (UTC).
Reliability of PM article has been questioned internally, it seems; related articles on neutrosophic sets and logic appear to have had WP versions deleted (they appear on google, but don't exist). So, this article does not seem appropriate for WP. Ben Cairns 05:59, 3 Feb 2005 (UTC).
See above AdamSmithee 14:08, 6 March 2006 (UTC)[reply]

60A99 Miscellaneous[edit]

Merged as a generalisation of Boole's inequality. Added redirect from Bonferroni inequalities. Ben Cairns 00:23, 16 Feb 2005 (UTC).
But see the entries proof of Borelli-Cantelli 1 and 2 below. Ben Cairns 02:41, 4 Feb 2005 (UTC).
Ben Cairns 03:03, 4 Feb 2005 (UTC).
... but could use some cleanup. Ben Cairns 03:12, 4 Feb 2005 (UTC).
Ben Cairns 03:19, 4 Feb 2005 (UTC).
Added in examples of medians of several common distributions. Ben Cairns 04:01, 4 Feb 2005 (UTC).
  • PM: mode, id=5889 -- WP guess: mode -- Status:
Simple cut-and-paste should suffice. Ben Cairns 00:57, 16 Feb 2005 (UTC).
Simple cut-and-paste should suffice. Ben Cairns 00:57, 16 Feb 2005 (UTC).
Ben Cairns 03:03, 4 Feb 2005 (UTC).
Ben Cairns 03:19, 4 Feb 2005 (UTC).
The PM article's definition is particularly restrictive and (possibly) obscure. The WP article seems adequate but I will defer to a better-informed reader. If you are familiar with the mathematics of this topic please check the articles and update this entry appropriately. Ben Cairns 04:43, 4 Feb 2005 (UTC).
WP article covers support more generally for functions and distributions. Noted that probability measures are measures. Ben Cairns 04:29, 4 Feb 2005 (UTC).

60Axx Foundations of probability theory[edit]

60B10 Convergence of probability measures[edit]

PM article explicitly uses a general metric for the difference between Xn and X but I don't think this is necessary here. Ben Cairns 08:28, 12 April 2006 (UTC)[reply]

60B11 Probability theory on linear topological spaces[edit]

A new article seems more appropriate than adding it to multivariate normal distribution. Ben Cairns 11:04, 6 Feb 2005 (UTC).

60Bxx Probability theory on algebraic and topological structures[edit]

60C05 Combinatorial probability[edit]

60D05 Geometric probability, stochastic geometry, random sets[edit]

60E05 Distributions: general theory[edit]

The WP article lacks the generating function of a binomial and the derivation of the mean and variance. Also needs refactoring and general clean-up! Ben Cairns 11:15, 6 Feb 2005 (UTC).
Article covers all major modes of convergence of random variables. Made a couple of edits, but it was essentially all there. Ben Cairns 11:47, 6 Feb 2005 (UTC).
Ben Cairns 11:53, 6 Feb 2005 (UTC)
User:Robbjedi
The PM article starts with probability 'density' (should be 'mass') functions for discrete distributions, then extends to probability density functions for continuous distributions. It seems (from a quick scan) to contain an error in constructing the latter. Ben Cairns 03:36, 7 Feb 2005 (UTC).
Ben Cairns 21:55, 7 Feb 2005 (UTC).
A little extra derivation in PM article, so I added the p.g.f. and a link. Ben Cairns 04:30, 16 Feb 2005 (UTC).
Long ago copied from PM; I added the copyright license notice. Ben Cairns 04:06, 16 Feb 2005 (UTC).
Plus some additional material on a more general version of the theorem. Ben Cairns 23:11, 17 Feb 2005 (UTC).
Ben Cairns 01:18, 15 Mar 2005 (UTC).
...following a couple of minor edits. Ben Cairns 01:32, 15 Mar 2005 (UTC).
AdamSmithee 14:36, 6 March 2006 (UTC)[reply]
AdamSmithee 14:36, 6 March 2006 (UTC)[reply]
AdamSmithee 14:36, 6 March 2006 (UTC)[reply]

60E07 Infinitely divisible distributions; stable distributions[edit]

60E10 Characteristic functions; other transforms[edit]

A bunch of properties of characteristic functions in the PM article do not appear in the WP article. Ben Cairns 12:00, 6 Feb 2005 (UTC).
We've needed this article for a while to complete the proof of the law of large numbers and the basic central limit theorem. Ben Cairns 12:00, 6 Feb 2005 (UTC).

60E15 Inequalities; stochastic orderings[edit]

Doesn't seem to appear elsewhere on WP. Ben Cairns 01:54, 16 Feb 2005 (UTC).
Done User:Robbjedi
...with the above article. Ben Cairns 01:54, 16 Feb 2005 (UTC).

60E99 Miscellaneous[edit]

Ben Cairns 11:48, 20 Feb 2005 (UTC).
Could use some refactoring to synthesise the section on the law of small numbers with the law of rare events. Also added link to PM article. Ben Cairns 12:13, 20 Feb 2005 (UTC).
PM article defines probability distribution functions as objects generalising both probability mass functions and probability density functions. Contrast common usage of distribution function as the cumulative distribution function, and probability distribution as something somewhat less general than a probability measure. Seems best merged with probability distribution, but we should stick with WP's established terminology (which I happen to be familiar with myself). Nonetheless, content from this article should make an excellent contribution. Ben Cairns 12:24, 20 Feb 2005 (UTC).

60Exx Distribution theory[edit]

60F05 Central limit and other weak theorems[edit]

There is some good content here, including a more general Lyapunov condition, that could be merged. The historical note is also interesting. Ben Cairns 12:37, 20 Feb 2005 (UTC).

60F15 Strong theorems[edit]

The non-i.i.d. case is not covered by the WP article. Ben Cairns 12:29, 20 Feb 2005 (UTC).
As part of the merge for Kolmogorov's strong law of large numbers, above. Ben Cairns 12:29, 20 Feb 2005 (UTC).

60F99 Miscellaneous[edit]

60Fxx Limit theorems[edit]

60G05 Foundations of stochastic processes[edit]

...but could use some work to make the notation clearer. Ben Cairns 03:33, 16 Feb 2005 (UTC).

60G07 General theory of processes[edit]

Ben Cairns 04:13, 16 Feb 2005 (UTC).

60G09 Exchangeability[edit]

60G10 Stationary processes[edit]

added redirect AdamSmithee 09:44, 28 September 2006 (UTC)[reply]
AdamSmithee 09:44, 28 September 2006 (UTC)[reply]

60G15 Gaussian processes[edit]

60G17 Sample path properties[edit]

60G40 Stopping times; optimal stopping problems; gambling theory[edit]

WP's article is less formal (it avoids talking about filtrations), but seems adequate in the context. The concept of a filtration could be added to the article, but this might as well be done organically. Ben Cairns 03:29, 16 Feb 2005 (UTC).
Ben Cairns 04:00, 16 Feb 2005 (UTC).

60G42 Martingales with discrete parameter[edit]

  • PM: gale, id=8948new! -- WP guess: gale -- Status:

60G44 Martingales with continuous parameter[edit]

60G46 Martingales and classical analysis[edit]

60G50 Sums of independent random variables; random walks[edit]

60G51 Processes with independent increments[edit]

60G60 Random fields[edit]

60G99 Miscellaneous[edit]

60Gxx Stochastic processes[edit]

60H05 Stochastic integrals[edit]

60H10 Stochastic ordinary differential equations[edit]

60H30 Applications of stochastic analysis (to PDE, etc.)[edit]

60H40 White noise theory[edit]

60H99 Miscellaneous[edit]

60Hxx Stochastic analysis[edit]

60J10 Markov chains with discrete parameter[edit]

Added a ref. to the PM article. Ben Cairns 03:46, 16 Feb 2005 (UTC).
PM article is specific to Markov chains, but hitting times are a common quantity of interest in many stochastic processes. Ben Cairns 03:46, 16 Feb 2005 (UTC).
Ben Cairns 03:24, 16 Feb 2005 (UTC).
This is specific to Markov chains, and is such a common problem in applications that it should be merged into that article. Ben Cairns 03:46, 16 Feb 2005 (UTC).

60J35 Transition functions, generators and resolvents[edit]

60J65 Brownian motion[edit]

60Jxx Markov processes[edit]

60K05 Renewal theory[edit]

60Kxx Special processes[edit]

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