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.

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

$\displaystyle 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 $

$\displaystyle R:=\exp\left\{\mu + \sum\limits_{j=1}^d \sigma B^j_h\right\}$

$\displaystyle \mu, \sigma$ are just constants.

Am I right, that $\displaystyle R_n$ are independent for $\displaystyle n=1,\ldots, N$ and $\displaystyle R_n\stackrel{d}{=}R$?

whrere $\displaystyle d$ denotes equality in distribution.

Thanks in advance!

Re: distribution of a product of lognormal distributed random variables

Hello,

I think you're right on both points.