  Regularity of the impulse control problem for a non-degenerate
$n$-dimensional jump diffusion with infinite activity and finite variation
jumps was recently examined by Davis, Guo, and Wu (SICON 2010). Here we extend
the analysis to include infinite activity and infinite variation jumps. More
specifically, we show that the value function $u$ of the impulse control
problem satisfies $u\in W^{2,p}_{\mathrm{loc}}(\mathbb{R}^{n})$.
