# distribution of a product of lognormal distributed random variables

• June 24th 2011, 12:49 PM
Juju
distribution of a product of lognormal distributed random variables
I'm sure, this question is very trivial. But I'm a little bit confused right now.

$B=(B_t^1,\ldots,B_t^d)$ is a d-dimensional Brownian motion.

$R_n:=\exp\left\{\mu + \sum\limits_{j=1}^d \sigma (B_{nh}^j-B^j_{(n-1)h})\right\} \quad n=1,2,\ldots,N$
$R:=\exp\left\{\mu + \sum\limits_{j=1}^d \sigma B^j_h\right\}$
$\mu, \sigma$ are just constants.
Am I right, that $R_n$ are independent for $n=1,\ldots, N$ and $R_n\stackrel{d}{=}R$?
whrere $d$ denotes equality in distribution.