Timeline for Convergence in law and distribution theory
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 28, 2022 at 17:16 | comment | added | Ben Deitmar | Correct, sorry! | |
| Feb 28, 2022 at 15:12 | history | edited | coudy | CC BY-SA 4.0 |
correct typo
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| Feb 28, 2022 at 12:55 | comment | added | coudy | @Tardis I am assuming here that the limit is the Fourier transform of a probability measure. Hence, no additional hypothesis is needed. | |
| Feb 28, 2022 at 10:15 | comment | added | Ben Deitmar | @coudy Yes, the definition is correct, but the convergence in distribution is only equivalent to the pointwise convergence of the characteristic functions when certain additional conditions are met. These conditions are not stated in the Wikipedia article about convergence in dirtibution (see en.wikipedia.org/wiki/…), but they are stated in the article about Levy's continuity theorem (see en.wikipedia.org/wiki/Lévy%27s_continuity_theorem). | |
| Feb 28, 2022 at 8:44 | comment | added | coudy | @Tardis My definition is correct. See here for the definition of the convergence in law (or convergence in distribution) en.wikipedia.org/wiki/… together with the portmanteau theorem. | |
| Feb 28, 2022 at 7:33 | comment | added | Ben Deitmar | Your formulation of the theorem for convergence in law is missing a tightness/continuity-condition. The correct formulation can be found here: en.wikipedia.org/wiki/Lévy%27s_continuity_theorem | |
| Feb 27, 2022 at 11:09 | review | Close votes | |||
| Mar 14, 2022 at 3:06 | |||||
| Feb 27, 2022 at 10:40 | comment | added | Mateusz Kwaśnicki | If you're OK with $f \in C_b^\infty$ rather than $f \in C_b$, then there is a concept of integrable distributions: functionals on $C_b^\infty$, which should give what you are looking for. This class is discussed already in L. Schwartz's Théorie des distributions (Hermann, Paris, 1966). | |
| Feb 27, 2022 at 10:32 | history | asked | coudy | CC BY-SA 4.0 |