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)Reply

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)Reply

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

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The claimed proposition refers to a conditional probability density, that is an expression of the form  . This is not well-defined, since  ; 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   involves quantification over   and therefore is not stochastically independent from the event  .

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

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

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.Reply

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.Reply

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".Reply

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.Reply

  • 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)Reply

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.Reply

--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.Reply

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.Reply