Is this the correct use of Girsanov's transformation where $B_{n}$ is a discrete Brownian motion?
For example computing:
$E[(B_{n}+2n)^{2}]$
Set: $\widetilde{B_{n}}=B_{n}+2n$
And use:$\frac{dQ}{dP}= Z = \exp(-2B_{n}-\frac{1}{2}(4)n)$
$E_{P}[(Z\widetilde{B_{n}})^2] = \widetilde{E}_{Q}[\widetilde{B_{n}}^2] = n$
since $\widetilde{B_{n}}$ has become a discrete Brownian motion under measure $Q$ and $\widetilde{E}_{Q}[\widetilde{B_{n}}^2] = \mathrm{Var}(\widetilde{B_{n}})$ under measure $Q$?
Thanks, trying to get a handle on this...
