Following up this question, assume $X_1$ to $X_n$ are $n$ correlated random variables with know marginal cumulative/probability distribution functions of $f_1(X_1)$ to $f_n(X_n)$, and a joint cumulative/probability density function of $f(X_1, ..., X_n)$.
What is the cumulative/probability density function of $y=X_1+...+X_n$?
One convolution formula is:
$$f_Y(y) = \iint\!\!\ddots\!\!\iint_{\Bbb R^{n-1}} f\left(x_1, x_2 , x_3, \ldots,x_{n-1}, y-\sum_{k=1}^{n-1} x_k\right)\operatorname d x_{n-1} \cdots \operatorname d x_1$$