Stochastic differential Im really new in the stochastic procceses please help me.
How can I solve this stochastic differential equation?
$$dX = A(t)Xdt$$
$$X(0) = X_0$$
If $A$:[0,$\infty$]$\to$ $R$ is continous and $X$ is a real random variable.

You would solve this equation like any other differential equation (assuming $X(t)\in\mathbb{R}^n\times[0,\infty)$), 
$X'(t) = A(t)X(t) \implies X(t) = \exp(A(t))X_0.$
The randomness of $X(t)$ must enter either through the initial condition $X_0$ or the function $A(t)$.  
