# What PDE does the physical measure sde solve?

I have two questions:

1)

Let's say I had an estimate of $$\mu$$ in an sde:

$$dZ = \mu Z dt + \sigma Z dW$$

If I ran monte carlo I could price say an option like $$Call_t = e^{-rT}E_t[(Z-k)+]$$

Feynman-Kac says that given a PDE of a certain form (see https://en.wikipedia.org/wiki/Feynman%E2%80%93Kac_formula)

then $$Call_t = e^{-rT}E_t[(Z-k)+]$$ and $$dZ = \mu(X, t) dt + \sigma(X,t)dW$$

The question is could I use that PDE to solve the above sde? Does feynman kac allow us to say if we have an SDE and an expectation it implies a PDE?

2)

Is there a way besides feynman-kac to write the PDE for the above SDE and expectation? For example, in the black-scholes paper they use delta hedging to write out a PDE

$$d\Pi = dCall - \frac{dCall}{ds}S$$ show that it has no risk so it must drift a $$r\Pi dt$$ then set the drifts equal to eachother to get the black scholes formula.

But there doesn't seem to be an equivalent argument for the physical measure.

Anyways I may be confusing myself, any help would be appreciated.