1. ## Prove this :(

I have an equation

$dS_{i}(t)=S_{i}(t)(\mu_{i}(t)dt+\sum^{d}_{k=1} \sigma_{ik}dW_{k}(t))$

We have a filtraiton $G_t$
Show that the expectation of $\frac{S_{i}(t+\triangle)-S_{i}(t)}{S_{i}(t)} |G_{t}=\mu_{i}(t)\triangle$

2. ## Re: Prove this :(

So I'm thinking the solution of the stochastic differntial equation is

$S_{i}(t)=S_{i}(0)e^{(\mu_{i}(t)-\frac{1}{2}(\sum_{k=1}^{d}\sigma_{ik}(t))^{2})t+(\ sum_{k=1}^{d}\sigma_{ik}(t)W_{k}(t))}$

But i'm not sure what to do next