the power variation of some fractional fields $(X_t)_{t\in {\mathbb{R}}^d}$. In the case $d=1$, they considers fractional Lévy processes $(X_t)_{t\in {\mathbb{R}}}$ of the form $$\label{eq:7237}
 X_t= \int_{{\mathbb{R}}} \big\{|t-s|^{H-1/2} - |s|^{H-1/2}\big\}\,dL_s$$ where $L$ is a truncated $\beta$-stable Lévy process. This setting is close to fit into the framework of the present paper with $\alpha= H-1/2$ except for the fact that the stochastic integral is over the hole real line. However, the proof of Theorem \[maintheorem\](i) still holds for $X$ in with obvious modifications of $h_k$ and $V_m$ in and , respectively. Notice also that [@BCI] considers the power variation along the subsequence $2^n$, which corresponds to dyadic partitions, and their setting includes second order increments. For $p<\beta$, Theorem 5.1 of [@BCI] claims that $2^{n \alpha p} V(p;2)_{2^n}\to C$ a.s. where $C$ is a positive constant, which in the notation of [@BCI] corresponds to the case $\alpha<\beta<2$. However, this contradicts Theorem \[maintheorem\](i) together with the remark following it, namely that, convergence in probability can not take place under the conditions of Theorem \[maintheorem\](i) not even trough a subsequence. The main part of the proof of the cited result, [@BCI Theorem 5.1], consists in proving that ${\mathbb{E}}[  2^{n\alpha p} V(p;2)_{2^n}] \to C$ (see p. 