this might sound like a stupid question but I'm trying to figure out how to write this Expectation in integral form:
$\mathbb{E}\left(\frac{1}{F( a + \sigma W_{T} + \sigma^{2}/2T)}\right) = \int\quad??$
where $F$ is just some function, and $a$, $T$ and $\sigma$ are arbitrary variables, and $W_{T}$ is a Brownian Motion random variable.
I honestly have no clue how to write it as an integral, I'm doing stats research so this stuff is a bit beyond what I've had to do, but I was told by another researcher that I had to use the heat kernel in the integral, however, as he is not currently at the uni he couldn't elaborate any further. I'd appreciate it if someone here could help me with this, thanks in advance