Timeline for convergence of integral for each bounded function in probability
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jun 5, 2015 at 6:58 | comment | added | Valentas | Thank you for comments and the examples. I had actually realised that an arbitrary convergent subsequence was sufficient for what I wanted to do (apply a result for deterministic sequence to a random sequence). | |
| Jun 5, 2015 at 6:44 | vote | accept | Valentas | ||
| May 31, 2015 at 8:39 | answer | added | Michael | timeline score: 0 | |
| May 31, 2015 at 0:02 | comment | added | Nate Eldredge | @Michael: See Example 4 here. | |
| May 31, 2015 at 0:01 | comment | added | Michael | @NateEldredge , what is the "standard typewriter sequence"? | |
| Apr 30, 2015 at 15:58 | comment | added | Nate Eldredge | Is it even true for real-valued random variables $X_n$ that if $X_n \to X$ i.p. then you can find an a.s. convergent subsequences which consists of almost all members in your sense? Is it true for the standard "typewriter sequence" counterexample? | |
| Apr 30, 2015 at 15:54 | comment | added | Valentas | By "consisting of almost all members" I mean is there, almost surely, a random set A such that $n^{-1} |A \cap \{1, .., n\}| \to 0$ and $\mu_{n, n\not \in A} \Rightarrow \mu$ (or something in this direction). Also I am interested in subsequences that converge to $\mu$ given in the assumption above. | |
| Apr 30, 2015 at 15:38 | comment | added | Nate Eldredge | I am not really sure what you mean by "consisting of almost all members", can you be more explicit? You can certainly say that there is a subsequence $(\mu_{n_k})$ which converges weakly almost surely; this is a standard fact for real-valued random variables and the proof works for random variables taking values in any metrizable topological space, such as the weak topology on a bounded set of measures on a Polish space. | |
| Apr 30, 2015 at 14:32 | history | edited | Valentas | CC BY-SA 3.0 |
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| Apr 30, 2015 at 14:26 | history | edited | Valentas | CC BY-SA 3.0 |
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| Apr 30, 2015 at 14:11 | history | asked | Valentas | CC BY-SA 3.0 |