I have the following process:
$Y_{t}=\left(W_{t}+\sqrt{Y_{o}}\right)^{2}$
That is the solution of the Îto SDE:
$d Y_{t}=d t+2 \sqrt{Y_{t}} d W_{t}, t \geq 0$
I want to convert this Îto SDE to a Stratonivitch SDE. The solution is:
$d Y_{t}=2 \sqrt{Y_{t}} d W_{t}, t \geq 0$
I am confused about both solutions. I included a screenshot of the course manual.
The manual says that the SDE becomes:
$d Y_{t}=d t+2\left(w_{t}+\sqrt{Y_{t}}\right) d w_{t}$ that is different than $d Y_{t}=2 \sqrt{Y_{t}} d W_{t}, t \geq 0$
My second question is about the conversion from ito to Stratonovitch. I don't understand how this conversion is done. For me it seems like they just removed the $dt$ term. Could somebody please help me understand the principle behind the conversion? Which steps do I need to take in order to get the conversion right?
Thanks in advance!