Doob's martingale convergence theorems: Revision history

15 May 2024

• curprev 11:0411:04, 15 May 2024 LucasBrown talk contribs 16,923 bytes +63 Adding local short description: "Theorems concerning stochastic processes", overriding Wikidata description "theorem" undo Tag: Shortdesc helper

31 October 2023

• curprev 09:0609:06, 31 October 2023 Citation bot talk contribs 16,860 bytes +38 Add: publisher. | Use this bot. Report bugs. | Suggested by Abductive | Category:Martingale theory | #UCB_Category 7/27 undo

27 July 2022

• curprev 14:2814:28, 27 July 2022 Citation bot talk contribs 16,822 bytes −53 Alter: url. URLs might have been anonymized. Add: s2cid, authors 1-1. Removed parameters. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by AManWithNoPlan | #UCB_CommandLine undo

28 September 2021

• curprev 16:5216:52, 28 September 2021 178.66.159.4 talk 16,875 bytes +4 In Doob's second martingale convergence theorem in definition of uniform integrability the absolute value of | N_t(\omega) | has to be under the integral, see https://en.wikipedia.org/wiki/Uniform_integrability undo

9 March 2021

• curprev 15:2815:28, 9 March 2021 Saibod talk contribs m 16,871 bytes +1 No edit summary undo

28 October 2020

• curprev 08:1508:15, 28 October 2020 WikiCleanerBot talk contribs m 16,870 bytes 0 v2.03b - Bot T20 CW#61 - WP:WCW project (Reference before punctuation) undo Tag: WPCleaner

31 May 2020

• curprev 05:0905:09, 31 May 2020 Mr.gondolier talk contribs 16,870 bytes 0 No edit summary undo

27 May 2020

• curprev 01:3001:30, 27 May 2020 2601:445:4380:7dd0:1b7:50e6:5871:f022 talk 16,870 bytes +8 →Convergence in Lp undo
• curprev 01:3001:30, 27 May 2020 2601:445:4380:7dd0:1b7:50e6:5871:f022 talk 16,862 bytes −2 →Doob's upcrossing inequality undo

9 February 2020

• curprev 09:4309:43, 9 February 2020 Hthrhthr12 talk contribs 16,864 bytes +131 →Doob's upcrossing inequality undo Tags: Mobile edit Mobile app edit Android app edit

30 January 2020

• curprev 02:2102:21, 30 January 2020 FrescoBot talk contribs m 16,733 bytes −29 Bot: link syntax undo

1 December 2019

• curprev 02:0702:07, 1 December 2019 Drohatgi talk contribs 16,762 bytes +61 →Doob's upcrossing inequality: corrected and clarified definition of U_n undo
• curprev 01:5101:51, 1 December 2019 Drohatgi talk contribs 16,701 bytes +186 →Statement for discrete-time martingales: corrected assertion about unprofitable strategies undo
• curprev 01:4201:42, 1 December 2019 Drohatgi talk contribs m 16,515 bytes 0 →Statement for discrete-time martingales undo
• curprev 01:4201:42, 1 December 2019 Drohatgi talk contribs 16,515 bytes +76 →Statement for discrete-time martingales: define negative part undo
• curprev 01:4101:41, 1 December 2019 Drohatgi talk contribs 16,439 bytes 0 link random variable undo
• curprev 01:4001:40, 1 December 2019 Drohatgi talk contribs 16,439 bytes +50 link almost sure convergence undo
• curprev 01:3101:31, 1 December 2019 Drohatgi talk contribs m 16,389 bytes +11 →Proof sketch undo
• curprev 01:3101:31, 1 December 2019 Drohatgi talk contribs 16,378 bytes −36 →Proof sketch: rephrasing for style undo
• curprev 01:2301:23, 1 December 2019 Drohatgi talk contribs 16,414 bytes −10 →Statement for discrete-time martingales undo
• curprev 01:1601:16, 1 December 2019 Drohatgi talk contribs 16,424 bytes +333 →Failure of convergence in mean: clarify why (Y_n) doesn't converge in mean to any RV undo

30 November 2019

• curprev 04:3704:37, 30 November 2019 Drohatgi talk contribs 16,091 bytes +13 →Failure of convergence in mean: clarify Y undo
• curprev 04:3604:36, 30 November 2019 Drohatgi talk contribs 16,078 bytes +1,727 added counterexample for martingale convergence in mean undo
• curprev 03:3103:31, 30 November 2019 Drohatgi talk contribs 14,351 bytes +81 →Proof sketch undo
• curprev 03:2803:28, 30 November 2019 Drohatgi talk contribs 14,270 bytes −33 →Statement for discrete-time martingales: redundant link undo
• curprev 03:2303:23, 30 November 2019 Drohatgi talk contribs 14,303 bytes +73 →Applications: put back anchor undo
• curprev 03:2203:22, 30 November 2019 Drohatgi talk contribs 14,230 bytes +251 →Doob's upcrossing inequality: martingale -> supermartingale; clarified significance of upcrossing inequality undo
• curprev 02:4902:49, 30 November 2019 Drohatgi talk contribs 13,979 bytes −458 →Doob's upcrossing inequality: simplified statement undo
• curprev 02:3602:36, 30 November 2019 Drohatgi talk contribs 14,437 bytes +25 →Lévy's zero–one law: math typesetting undo
• curprev 02:2702:27, 30 November 2019 Drohatgi talk contribs m 14,412 bytes −12 →Doob's upcrossing inequality: math typesetting undo
• curprev 02:2502:25, 30 November 2019 Drohatgi talk contribs 14,424 bytes −49 →Convergence in Lp: math typesetting undo
• curprev 02:2202:22, 30 November 2019 Drohatgi talk contribs 14,473 bytes −150 →Statements for the general case: math typesetting undo
• curprev 02:0702:07, 30 November 2019 Drohatgi talk contribs 14,623 bytes +29 →Proof sketch: clarify what sequence refers to undo
• curprev 02:0502:05, 30 November 2019 Drohatgi talk contribs m 14,594 bytes +1 →Proof sketch undo
• curprev 02:0502:05, 30 November 2019 Drohatgi talk contribs 14,593 bytes 0 →Proof sketch undo
• curprev 02:0002:00, 30 November 2019 Drohatgi talk contribs 14,593 bytes −10 "long-time" doesn't seem to add meaning undo
• curprev 01:3101:31, 30 November 2019 Drohatgi talk contribs 14,603 bytes +71 clarified "sub/super-martingales" in introduction undo
• curprev 01:1601:16, 30 November 2019 Drohatgi talk contribs 14,532 bytes +34 moved "Convergence in L^p" to "Applications" section; reworded intuition for convergence undo
• curprev 01:1301:13, 30 November 2019 Drohatgi talk contribs 14,498 bytes −28 →Doob's upcrossing inequality: removed "Hypothesis" and "Conclusion"; reformatted undo

29 November 2019

• curprev 22:3122:31, 29 November 2019 Drohatgi talk contribs 14,526 bytes −92 reorganize -- applications after upcrossing inequality; L_p --> L^p undo
• curprev 21:1721:17, 29 November 2019 Drohatgi talk contribs 14,618 bytes +13 Rewording. Previous edit deleted statement about L_p convergence of discrete-time martingales, since it's essentially identical to statement for continuous martingales, and added sentence to this effect. undo
• curprev 21:1121:11, 29 November 2019 Drohatgi talk contribs 14,605 bytes −505 moved statement about convergence undo
• curprev 20:5820:58, 29 November 2019 Drohatgi talk contribs 15,110 bytes +256 →Statement for discrete-time martingales: motivation for expectation bound undo
• curprev 20:5120:51, 29 November 2019 Drohatgi talk contribs 14,854 bytes +1,338 Added the most common statement of the theorem, and some intuition for why it is true before proof sketch. Improved math typesetting of proof sketch. undo
• curprev 19:2719:27, 29 November 2019 Drohatgi talk contribs 13,516 bytes +456 expand introduction undo
• curprev 02:1702:17, 29 November 2019 Drohatgi talk contribs 13,060 bytes +61 No edit summary undo
• curprev 02:0202:02, 29 November 2019 18.20.210.231 talk 12,999 bytes +20 No edit summary undo
• curprev 02:0102:01, 29 November 2019 18.20.210.231 talk 12,979 bytes +6 No edit summary undo
• curprev 01:5901:59, 29 November 2019 Drohatgi talk contribs 12,973 bytes +2,801 Add intuition/sketch of proof for discrete-time bounded martingale convergence undo

9 November 2019

• curprev 21:2921:29, 9 November 2019 2601:445:4380:7dd0:932:380c:461a:5f79 talk 10,172 bytes +5 →Doob's upcrossing inequality undo