Before revision:  for which there is a well known closed-form formula in terms of the SVI parametrization}\hspace{0pt}%DIFAUXCMD . Finally, using L\'{e}vy's convergence theorem, we show that the log stock price X_t tends weakly to a non-symmetric random variable X^{(1/2)}_t as \alpha }\to \to _t/\sqrt{t} tends weakly to a non-symmetric random variable as t}\to \to  }\hspace{0pt}%DIFAUXCMD where the skew flattens or blows up) and the V process converges on pathspace to a random tempered distribution} .
After revision:  for which there is a well known closed-form formula in terms of the SVI parametrization}\hspace{0pt}%DIFAUXCMD . Finally, using L\'{e}vy's convergence theorem, we show that the log stock price X_t tends weakly to a non-symmetric random variable X^{(1/2)}_t as \alpha }\to \to 0) whose mgf is also the solution to the Rough Heston VIE with \alpha=1/2, and we show that X^{(1/2)_t/\sqrt{t} tends weakly to a non-symmetric random variable as t}\to \to }\hspace{0pt}%DIFAUXCMD where the skew flattens or blows up) and the V process converges on pathspace to a random tempered distribution} .