# Ito's formula with a random jump measure

Suppose all processes and functions defined are nice enough such that all the following definitions make sense.

On a probability space $$(\Omega,\mathcal{F},\mathbb{P})$$ equipped with a filtration $$\mathbb{F}$$ satisfying the usual conditions of right continuity and $$\mathbb{P}$$ completeness, let $$M$$ be a continuous $$\mathbb{F}$$ martingale and $$A$$ a continuous $$\mathbb{F}$$ adapted process of finite variation. Now let $$(E,\mathcal{B}(E))$$ be a measurable Lusin space. Now let $$\mu$$ be a random measure on the space $$(\Omega\times E,\mathcal{F}\times \mathcal{B}(E))$$ and $$\nu$$ its compensator. For $$\mathcal{P}$$ measurable processes $$\phi$$ and $$\psi$$, and a $$\mathcal{P}\otimes\mathcal{B}(E)$$ measurable process $$\beta(\cdot)$$. Define the semi-martingale $$X$$ by $$X_t = X_0 + \int_0^t\phi_s dA_s + \int_0^t\psi_sdM_s + \int_0^t\int_E \beta_s(e)(\mu(ds,de)-\nu(ds,de)).$$

Now suppose $$f$$ is a twice continuously differentiable function, how do I apply Ito's formula to get the semi-martingale decomposition of $$f(X_t)$$? i.e. how do I calculate $$df(X_t) = ...?$$.