Before revision:  In the presence of a Brownian component, the second-order term, in time-t, is of the form d_{2}  t^{(3-Y)/2}, with the coefficient d_{2 on Y, the degree of jump activity, on \sigma, the volatility of the continuous component, and on an additional parameter controlling the intensity of the "small" jumps (regardless of their signs).
After revision:  In the presence of a Brownian component, the second-order term, in time-t, is of the form d_{2} \, t^{(3-Y)/2}, with the coefficient d_{2 on Y, the degree of jump activity, on \sigma, the volatility of the continuous component, and on an additional parameter controlling the intensity of the "small" jumps (regardless of their signs).