Originally Posted by

**danlfnce** Hi all,

I hope this is the right forum for this -- if not, it would be nice if someone can tell me where I should post this.

Suppose $\displaystyle dx_{t}/x_{t}=\mu dt+\sigma_{t}dB_{t} $ , where B is the standard Brownian motion, and where $\displaystyle \sigma_{t}\in\{\sigma_{H},\sigma_{L}\}$

with transition probability matrix between t and t+dt:

$\displaystyle P=\left(\begin{array}{cc}p & 1-p\\1-q & q\end{array}\right)dt $

- what is $\displaystyle E[x_{t}|\sigma_{0}=\sigma_{H}] $?

- what is $\displaystyle E[x_{t}^{\alpha}|\sigma_{0}=\sigma_{H}] $?

Thanks!

Dan