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Math Help - distribution of a product of lognormal distributed random variables

  1. #1
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    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.

    Thanks in advance!
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  2. #2
    Moo
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    Re: distribution of a product of lognormal distributed random variables

    Hello,

    I think you're right on both points.
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