What is the definition of mu(X(t),t)?

Discussion in 'CM2' started by Johnson Adeleke, Aug 14, 2019 at 8:13 AM.

If I have an equation X(t) = mu(t)dt + sigma(t)dW(t) and it says in ITO's Lemma mu(X(t),t) does that mean E(X(t))?

2. Steve HalesActEd TutorStaff Member

Hi
The LHS of your equation needs an extra d, ie: dX(t) = mu(t)dt + sigma(t)dW(t).
The mu in Ito's Lemma refers to the drift term in the SDE of X(t), not the expected value of X(t).
From your equation it appears that mu is only a function of time, so in Ito's Lemma you only need mu(t) rather than mu(X(t),t).
Maybe post the full example, that way it will be easier to explain what's required?
Thanks
Steve