What are the distribution (or density) functions of processes defined by

$dX_t=\mu dt +\sigma dW_t$

and

$dX_t= \theta(\mu-X_t) dt +\sigma dW_t,$

where $\theta>0$, $\mu$ is a real number, $\sigma>0$

I know it is a solved problem, but I cannot find a reference that presents the detailed steps of the derivations. Could you please provide some good references? Or, could you please come with the derivations?

What are the transition distribution (or density) functions of processes defined by

$dX_t=\mu dt +\sigma dW_t$

and

$dX_t= \theta(\mu-X_t) dt +\sigma dW_t,$

where $\theta>0$, $\mu$ is a real number, $\sigma>0$, and $W_t$ is a standard Brownian motion.

I know it is a solved problem, but I cannot find a reference that presents the detailed steps of the derivations. Could you please provide some good references? Or, could you please come with the derivations?

What are the distribution (or density) functions of processes defined by

where $\theta>0$, $\mu$ is a real number, $\sigma>0$

I know it is a solved problem, but I cannot find a reference that presents the detailed steps of the derivations. Could you please provide some good references? Or, could you please come with the derivations?

What are the distribution (or density) functions of processes defined by

$dX_t=\mu dt +\sigma dW_t$

and

$dX_t= \theta(\mu-X_t) dt +\sigma dW_t,$

where $\theta>0$, $\mu$ is a real number, $\sigma>0$

I know it is a solved problem, but I cannot find a reference that presents the detailed steps of the derivations. Could you please provide some good references? Or, could you please come with the derivations?

What are the distribution (or density) functions of processes defined by

$dX_t=\mu dt +\sigma dW_t$

and

$dX_t= \theta(\mu-X_t) dt +\sigma dW_t,$

where $\theta>0$, $\mu$ is a real number, $\sigma>0$

I know it is a solved problem, but I cannot find a reference that presents the detailed steps of the derivations. Could you please provide some good references? Or, could you please come with the derivations?

What are the distribution (or density) functions of processes defined by

where $\theta>0$, $\mu$ is a real number, $\sigma>0$

I know it is a solved problem, but I cannot find a reference that presents the detailed steps of the derivations. Could you please provide some good references? Or, could you please come with the derivations?