# Ito's formula

1. Jan 19, 2009

### InvisibleBlue

Hi,

I'm trying to answer this question on why we can apply Ito's formula to the function $$F(Z_{t}, S_{t}, B_{t})$$ which is a $$C^{1,1,2}$$ function where:

$$B_{t}$$ is standard brownian motion

$$S_{t}=max_{0\leq s\leq t}B_{s}$$
and
$$Z_{t}= \int_0^t B_{s} ds$$

I think I basically have to show that $$S_{t}$$ and $$Z_{t}$$ are continuous and of bounded variation. But can't quite see how to show either, specially in the case of $$S_{t}$$ since we know that the standard brownian motion is not of bounded variation.

any ideas?