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- #1

- Thread starter gnob
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- Thread starter
- #1

- Feb 13, 2012

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Please, can You better explain what is theGood day!

I have a question regarding the law of the ff:

$$

\int_0^t h(s) e^{2\beta(\mu(s) + W_s)}

$$

where $\beta >0;$ $h,\mu$ are continuous functions on $\mathbb{R}_+$ with $h\geq 0;$

and $W=\{W_s,s\geq 0\}$ is a standard Brownian motion.

Thanks for any help.

Kind regards

$\chi$ $\sigma$

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- #3

Many thanks for the reply. What I meant of "law" is the probability density of the given integral. For the case $\mu(s) = -\nu s$ where $\nu$ is a positive constant and $h(s)=1,$ the law was already known (Corollary 1.2, p95) from Mar Yor's book given here Exponential Functionals of Brownian Motion and Related Processes - Marc Yor - Google Books .Good day!

I have a question regarding the law of the ff:

$$

\int_0^t h(s) e^{2\beta(\mu(s) + W_s)}

$$

where $\beta >0;$ $h,\mu$ are continuous functions on $\mathbb{R}_+$ with $h\geq 0;$

and $W=\{W_s,s\geq 0\}$ is a standard Brownian motion.

Thanks for any help.

Thanks again for any insights.