Timeline for Can we say that: $ \sum_{n\geq 1}{\frac{1}{n}(f_n(\omega)-g_n(\omega))}<\infty\qquad a.e $
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| May 23, 2020 at 20:51 | comment | added | Yuval Peres | Maybe you can attach a scan of the relevant pages. There could be additional assumptions there that would imply the desired conclusion. | |
| May 19, 2020 at 15:39 | comment | added | Parc John | But in book Two-Scale Stochastic Systems Asymptotic Analysis and Control by Kabanov, Yu.M., Pergamenshchikov, S, on page 254, the author says that: the series $$\sum_{k=1}^{\infty}{\zeta_{k}^{(k)}-\eta_k}$$ converges a.s with $\zeta^{(c)}=\zeta 1_{\{|\zeta|\leq c\}}$. Since only a finite number of $\zeta_{k}^{(k)}(\omega)$ is different from $\zeta_{k}(\omega)$, the series $$\sum_{k=1}^{\infty}{\zeta_{k}-\eta_k}$$ also converges a.s. | |
| May 19, 2020 at 4:37 | history | answered | Yuval Peres | CC BY-SA 4.0 |