A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is
If the space Q of quadratic forms in R n is splitted in a direct sum Q 1 ⊕ · · · ⊕ Q k and if X and Y are independent random variables of R n , assume that there exist a real number a such that E(X|X + Y ) = a(X + Y ) and real distinct numbers b 1 , ..., b k such that E(q(X)|X + Y ) = b i q(X + Y ) for any q in Q i . We prove that this happens only when k = 2, when R n can be structured in a Euclidean Jordan algebra and when X and Y have Wishart distributions corresponding to this structure.doi:10.24033/bsmf.2603 fatcat:2zxt7bjr6rg7dfb4ouvbeuspoi