Before revision:  In contrast, under  a pure-jump tempered stable model, the dependence on the overall jump intensity and Y is already reflected in the leading term, which is of the form d_{1} t^{1/Y}.
After revision:  In contrast, under a pure-jump model, the dependence on the overall jump intensity and Y is already reflected in the leading term, which is of the form d_{1} t^{1/Y}.