Multivariate log-normal distribution [duplicate]

Let $X=\mu + \Sigma^{1/2}Z$ and $Z\sim \mathcal{N}(0,I)$. Is there a closed form for the distribution of $\exp(X)$?

• by $\exp(X)$ do you mean the componentwise $\exp$? – Juho Kokkala May 3 '16 at 6:49
• Yes. I mean componentwise – user2808118 May 3 '16 at 6:49
• I'm not familiar with the notation capital sigma to the 1/2. I realize you're taking a sum, but what exactly are you summing? – barrycarter May 3 '16 at 16:05
• Sigma is the covariance matrix – user2808118 May 3 '16 at 16:07
• Basically, X is normally distributed with mean mu and covariance matrix Sigma – user2808118 May 3 '16 at 16:09