# SDE of the Lévy process

I consider a Lévy process of the form $$X_t = X_0 e^{(\mu-\frac{\sigma^2}{2})t+\sigma B_t-\sum_{i=1}^{N_t} Y_i},$$ where $$\mu$$ and $$\sigma$$ are constants, $$B_t$$ is a Brownian motion, $$N_t$$ is a Poisson process and $$Y_i$$ are i.i.d. random variables indepentent with $$N_t$$.

In different papers I noted that the Lévy process can be described as a solution of $$dX_t = \mu(t, X_t)dt + \sigma(t, X_t)dB_t+ \int_{\mathbb{R}}\gamma(t, X_t, z)\tilde{v}(dt, dz),$$ where $$\tilde{v}(dt, dz)$$ is a compensated Poisson measure.

My question is: What SDE satisfies process $$X_t$$ and how can I derive it?