Marginal Distribution of Diffusion Process

47 Views Asked by At

Working on a problem that I'm having some trouble starting. I have $X_t = 2t + 3B_t$ for $t \ge 0$ where $B_t$ is a Brownian Motion. I want to find the marginal distribution of $X_t$, as well as $E(X_s * X_t)$ for $s < t$. I'm pretty sure for the marginal distribution I need to apply Ito's formula, but I'm not exactly sure where to do this. Any help appreciated, thanks!