I have a random variable $X$ that is a sum of two non-independent random variables $X_1$ and $X_2$. Since $X_1$ and $X_2$ are non-independent, then convolution theorem cannot be used to find the pdf of $X$. With no other information on the relationship (covariance, etc) between $X_1$ and $X_2$, then it is ultimately difficult to derive the pdf of $X$. The distributions of $X_1$ and $X_2$ , however, are individually known.
So another 'strategy' must be used in order to derive the pdf of $X$. Fortunately, technology is available (Matlab) for simulations and histograms are made to run again and again. Now that we will be basing the pdf of $X$ from histograms, then I believe the correct word now should be 'estimating' the pdf of $X$.
Would you know of techniques that I should do/perform to be able to get this estimated pdf of $X$?