A Multivariate Faa di Bruno Formula with Applications
Gregory M. Constantine, Thomas H. Savits · Transactions of the American Mathematical Society · 1996
A multivariate Faa di Bruno formula for computing arbitrary partial derivatives of a function composition is presented. It is shown, by way of a general identity, how such derivatives can also be expressed in the form of an infinite series. Applications to stochastic processes and multivariate cumulants are then delineated.