Consider the Brownian semi-martingale
$$ p_t = \int_0^t\mu_s\,ds+\int_0^t\sigma_s\,dW_s, $$ where $\mu$ and $\sigma$ are cadlag processes and $W$ is a Brownian motion. Do there exist sufficient conditions for $\mu$ and $\sigma$ to guarantee that $p_t\geq 0$ path-wise?