A nonclassical solution to a classical SDE and a converse to Kolmogorov's zero–one law

Vidmar, Matija (author)

For a discrete-negative-time discrete-space SDE, which admits no strong solution in the classical sense, a weak solution is constructed that is a (necessarily nonmeasurable) non-anticipative function of the driving i.i.d. noise. The result highlights the strong rôle measurability plays in (non-discrete) probability. En route one — quite literally — stumbles upon a converse to the celebrated Kolmogorov’s zero–one law for sequences with independent values.

• Language: English
• Keywords: stochastic equations, equiprobable random signs, non-anticipative weak solutions, nonmeasurable sets, Kolmogorov's zero–one law
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2021
• Number of pages: 6 str.
• Numbering: Vol. 175, art. 109117
• PID: 20.500.12556/RUL-138678
• UDC: 519.216
• ISSN on article: 0167-7152
• DOI: 10.1016/j.spl.2021.109117
• COBISS.SI-ID: 61497347
• Publication date in RUL: 09.08.2022

Record is a part of a journal

• Title: Statistics & probability letters
• Shortened title: Stat. probab. lett.
• Publisher: Elsevier
• ISSN: 0167-7152
• COBISS.SI-ID: 1248533

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

• Language: Slovenian
• Keywords: stohastične enačbe, enako verjetni slučajni predznaki, neanticipirajoča šibka rešitev, nemerljive množice, Kolmogorov zakon nič – ena

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0402
• Name: Matematična fizika