Talk:Wiener process

message: No, only copy, resum, and cite Wiener process as main article.  —Preceding unsigned comment added by 201.52.194.78 (talk) 15:24, 4 February 2008 (UTC)
thread_title:  Merge with Brownian motion? 

message: I believe that Subsection 2.1 "Derivation" is of little interest and should be deleted.
However, I hesitate to do it myself. Maybe I find it uninteresting only because I am an expert already? Boris Tsirelson (talk) 08:59, 26 September 2008 (UTC)
replies: text: I think it should be kept for those less expert, but I have revised the sub-sectioning so that "Derivation" does not appear as a heading. Melcombe (talk) 09:32, 3 June 2009 (UTC)
thread_title:  To delete or not to delete? 

message: From the article: "W_t is almost surely continuous"
Is this
"Almost surely, W is continuous."
or
"For all t, W_t is almost surely continuous at t."
?  —Preceding unsigned comment added by JumpDiscont (talk • contribs) 21:03, 5 October 2009 (UTC)
replies: text: It is the former: "Almost surely, W is continuous." Boris Tsirelson (talk) 07:02, 6 October 2009 (UTC)
thread_title:  Continuity 

message: I added the joint distribution of the maximum and the Wiener process and included an integral to get the unconditional distribution of the maximum. I calculated this by hand, so I would appreciate if someone else confirmed it. I haven't seen it anywhere on the net.
108.35.46.175 (talk) 03:00, 11 April 2012 (UTC)
replies: text: Oops, no, something must be wrong with it. The (unconditional) distribution of M_t is much easier to get (than the joint distribution) by the reflection principle. It is distributed like |B_t|. Boris Tsirelson (talk) 05:57, 11 April 2012 (UTC)
replies: text:  Yeah I fixed it. Makes sense now. Mathematica to the rescue.  — Preceding unsigned comment added by 71.251.222.105 (talk) 13:58, 11 April 2012 (UTC)
replies: text:  OK. Boris Tsirelson (talk) 18:27, 11 April 2012 (UTC)
thread_title:  running maximum distribution 

message: I just want to thank User:Cyp for his nice new picture. Boris Tsirelson (talk) 17:38, 2 December 2009 (UTC)
replies: text: Glad you like it. (: Κσυπ Cyp   21:43, 2 December 2009 (UTC)
thread_title:  Thanks 

message: I deleted a section on the Fourier series. The formula given looked very wrong, and no reference was given. If someone knows the correct version, please update. 130.235.3.80 (talk) 10:29, 30 October 2013 (UTC)
replies: text: But see Karhunen–Loève theorem#The Brownian bridge. Boris Tsirelson (talk) 17:15, 30 October 2013 (UTC)
thread_title:  Fourier series 

message: It should be stated that the unconditional distribution function of the running maximum is defined only on [0,+∞). --Baroc (talk) 22:57, 26 February 2014 (UTC)
replies: text: OK, I did so. (Density you mean, not distribution function.) But now it looks rather repetitive, since the same restriction is mentioned on the previous display. Boris Tsirelson (talk) 06:41, 27 February 2014 (UTC)
thread_title: Running maximum distribution (2)

message: It is written that W has Gaussian increments: Wt+u - Wt is normally distributed with mean 0 and variance u, Wt+u−Wt ~ N(0, u)
However, later it is written that variance is t. Perhaps then notation should be Wt+u−Wt? ~ N(0, sqrt(u)) (assuming usual normal distribution notation) --92.42.31.61 (talk) 16:02, 2 January 2016 (UTC)
replies: text: No, the "usual normal distribution notation" is N(μ, σ2), not N(μ, σ) (as you probably believe); see Normal_distribution#Notation. Boris Tsirelson (talk) 18:08, 2 January 2016 (UTC)
thread_title:  Possible error 

message: I am a learner, I myself  need a reference for this sentence in Paragraph 3:  
"It also forms the basis for the rigorous path integral formulation of quantum mechanics     " 
Can anyone help?  — Preceding unsigned comment added by Davy2016 (talk • contribs) 03:42, 23 December 2016 (UTC)
thread_title:  A reference is wished 

message: In the section "Qualitative properties", it says that for any \epsilon > 0, w(t) is almost surely not (\tfrac 1 2 + \epsilon)-Hölder continuous. But it seems that we can do better: perhaps w(t) is almost surely not \tfrac 1 2-Hölder continuous? I have seen this claim in a comment to this Math Overflow question without proof. Is this result correct? 129.104.241.198 (talk) 15:49, 3 September 2023 (UTC)
thread_title:  The sample paths are almost surely not <math>\tfrac 1 2</math>-[[Hölder continuous]]?