Stash

$$\begin{align}
\delta' &\ge \frac{\delta}{4 }\left(\frac{\delta}{2}\right)^{\frac{a}{a-1}} \exp\left(\frac{-a \pi Q (T-t+1)N c^2 \alpha^2}{\sigma^2}\right) \\&= \frac{1}{2 }\left(\frac{\delta}{2}\right)^{\frac{2a-1}{a-1}} \exp\left(\frac{-a \pi Q (T-t+1)N c^2 \alpha^2}{\sigma^2}\right) \\\implies 2\delta'\left(\frac{\delta}{2}\right)^{\frac{1-2a}{a-1}} &\ge \exp\left(\frac{-a \pi Q (T-t+1)N c^2 \alpha^2}{\sigma^2}\right) \\\implies \ln\left(2\delta'\left(\frac{\delta}{2}\right)^{\frac{1-2a}{a-1}}\right) &\ge \frac{-a \pi Q (T-t+1)N c^2 \alpha^2}{\sigma^2} \\\implies \sigma^2 &\ge \frac{-a \pi Q (T-t+1)N c^2 \alpha^2}{\ln\left(2\delta'\left(\frac{\delta}{2}\right)^{\frac{1-2a}{a-1}}\right)} \\\implies \sigma &\ge \sqrt{\frac{-a \pi Q (T-t+1)N c^2 \alpha^2}{\ln\left(2\delta'\left(\frac{\delta}{2}\right)^{\frac{1-2a}{a-1}}\right)}} \\\end{align}$$