Talk:Probability distribution of extreme points of a Wiener stochastic process

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Hi Michael, you changed "extrema" with "extreme". I meant "extrema" as either "maxima" or "minima".

Extremum, plural Extrema, in calculus, any point at which the value of a function is largest (a maximum) or smallest (a minimum). There are both absolute and relative (or local) maxima and minima.Jul 20, 1998 extremum | mathematics | Britannica.com https://www.britannica.com/topic/extremum

See also: https://en.wikipedia.org/wiki/Maxima_and_minima

So would you reconsider the change, considering the above?

Ballad2 (talk) 22:51, 20 December 2016 (UTC)

Issue clarified: nouns used as adjectives are not supposed to be declined (singular vs. plural) in English. Ballad2 (talk) 09:33, 21 December 2016 (UTC)

Mathematical errors, I am afraid: request deletion...

The claimed proposition refers to a conditional probability density, that is an expression of the form $\Pr(Y\leq y\mid X=x)$. This is not well-defined, since $\Pr(X=x)=0$; see Conditional_probability_distribution#Conditional_continuous_distributions.

Reference 1 is not related, reference 2 is the 1978 PhD thesis of the page creator in Italian, reference 3 is not related.

Equation (2.5) in the "Constructive proof" is wrong, and so is most of what follows.

For example $E_{n}$ involves quantification over $t_{\nu }$ and therefore is not stochastically independent from the event $(X(b)-X(t_{\nu })<-X_{b}+z)$.

The left-hand side of Equation (2.14) depends on $a$, but the right-hand side does not: error.

Martin Ziegler (talk) 16:31, 16 March 2019 (UTC)

Ballad2 (talk) 21:21, 16 March 2019 (UTC) => See Regular conditional probability for a different point of view. References 1 and 3 to the formula are correct, need some time to review your other remarks.

Ballad2 (talk) 22:07, 16 March 2019 (UTC) I over simplified the proof of equation 2.5, a better proof is in reference 1, appendix 3 and the final formula for the distrubution (indicated as "35" in appendix 3 of the paper) is there as well.

Ballad2 (talk) 17:47, 21 March 2019 (UTC) About equation (2.14), X(b) is a normal random variable with average X(a) and variance proportional to (b-a), so the right-hand does depend on "a".

Ballad2 (talk) 10:22, 17 March 2019 (UTC) From what you write, I understand that you have no access to the paper in reference 1, would you like me to mail you a copy so you can check yourself? Your remark about proof of equation 2.5 is correct, but I can fix it according to reference 1. After this please remove the request for deletion, so we have time to fix the page.

• I removed the PROD nomination, because I believe this *might* turn into an interesting article, and it, also might, have a better chance being improved than deleted and recreated later on. My main issue is that it is way too much a technical mathematical paper, and too little and encyclopaedia entry. I know mathematicians tend to be very terse, I experience it personally as I am more than half way through a math degree right now (just did basic Stochastic Processes, that is how this caught my I :-). In a encyclopaedia article I think we need much less mathematical detail - just stick to a sketch of the proof - on the other hand we would need some hint of significance, i.e. applications, either practical or theoretical, and most of all of indications of wp:Notability, i.e., more than the derivation of the distribution, references to it elsewhere. - Nabla (talk) 22:34, 17 March 2019 (UTC) PS: pinging: @Ballad2 and Martin Ziegler: - Nabla (talk) 22:37, 17 March 2019 (UTC)

Ballad2 (talk) 00:06, 18 March 2019 (UTC) I see the point, but as a matter of fact from the "sketch of the proof" in reference 1 to the explanation in this article there were weeks of research. I published this proof in Wikipedia so it could be checked and improved by other mathematicians. I am not aware of any other paper with a proof of this theorem, so it is probably worth to keep it here.

--Ballad2 (talk) 17:47, 21 March 2019 (UTC) I did a major review of the proof compared to the original 1978 version. It is now greatly simplified and weakness in the (2.5) proof has been fixed.

• @Ballad2: I am afraid that wikipedia is not the place to publish your reearch, no matter how interesting it may be (and it is interesting). I guess you could get help from your university, maybe publish at the arxiv, get a personal site, or... something. But publishing wp:Original Research is not one of Wikipedia's goals @Martin Ziegler: - Nabla (talk) 15:40, 21 April 2019 (UTC)

Ballad2 (talk) 18:43, 21 April 2019 (UTC) I probably misused the word "research". I meant it took me weeks to understand the H.J. Kushner proof and expand all steps to a level of detail that everybody with minimal probability background could easily follow. This is not original research, the formula for the distribution is fully described th the H.J. Kushner paper.