From: Colin Rowat on
I would like to compute the distribution of X_1 + ... + X_T, where
each X_t is IID multivariate Student's t(nu,Mu,Sigma), or just MVT
(nu). If f is their pdf, I wish to do this by:

(a) computing phi = F(f), the FFT of f; and
(b) computing f_T = F^{-1}(phi^T), the IFFT of phi^T.

I have two conceptual questions, and would be grateful for any advice:

1. in one dimension, one can identify the line with a circle before
taking step (a), above. In two dimensions, should the plane become a
toroid, a sphere, a cylinder, or something else yet? (Do higher
dimensions follow obviously?)

2. what pattern should I expect for the e^{pi i} terms in step (b)? I
have conjectured a checkerboard of [1 -1 1...] but wonder if I should
expect complex roots of unity.

My output looks plausible, but chops f_T over both edges of the plane.
I am therefore trying to understand whether this is more likely to
result from my treatment of end effects, or my checkerboard pattern.
(I am happy to send my code.)

Thank you in advance,

Colin Rowat
Department of Economics, University of Birmingham