I am recently into copulas for finance, I've read several examples of how to generate dependent random variables with most kind of copulas. The problem for me is that all the books describe the case with 2 random variables $(X_1,X_2)$ but I want to generate $n$ dependent r.v. $(X_1,X_2,\ldots,X_n)$.
I find the case easy for gaussian copulas, since we just have to expand the correlation matrix, apply cholesky decomposition and calculate matrix multiplication.
But I couldn't find a way to apply this for the case of a clayton copula, since the book examples always use the conditional copula density of r.v. #1 to generate r.v. #2. This seems not like a practical approach for multi r.v.
Is there some approach like the one for the gaussian copula?