I need help. I'm studying Lévy processes and one of the examples is the inverse gaussian process.

Let $(B_t)_{t\geq 0}$ a Brownian motion and define the first passage time

$\tau_s=inf\{t\geq 0: B_t+ct>s\}$.

Then $\tau=(\tau_s)_{s>0}$ is a Lévy process and $\mathbb{E}\left[e^{iz\tau_s}\right]=exp(s\sqrt{c^2-2iz}-c)$.

So my questions are:

- What is the the Lévy Khintchine representation, i.e. what is the generating triplet $(a,b,\nu)$ of this proces?
- What is the Lévy-Ito decomposition?

Thank you