Ito formula for $f(X_t, Y_{t-s})$

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I have a situation where I have two stochastic processes (say 2 OU processes) and I have the function $f(X_t, Y_{t-s})=\frac{X_t}{Y_{t-s}}$.

How do I apply Ito lemma in this case?(is Ito lemma still valid?)

This might be a very basic question for some of you here, so a reference would be enough if you can't be bothered to answer the question. Thank you.

Edit: I forgot to mention that there is a relation between $X_t$ and $Y_t$ in the sense that their driving BMs are correlated.