Before revision:  In the presence of an additional Brownian component, the second-order term, in time-t, is of the form d_{2} t^{(3-Y)/2}, with the coefficient d_{2} depending only on the overall jump intensity of the process and the tail-heaviness parameter Y. This extends the already known result that the leading term is \sigma t^{1/2/2\pi, where }  the volatility of the continuous component  .
After revision:  In the presence of an additional Brownian component, the second-order term, in time-t, is of the form d_{2} t^{(3-Y)/2}, with the coefficient d_{2} depending only on already known result that the leading term is \sigma t^{1/2/2\pi, where } the volatility of the continuous component .