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

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

  1. Johnson Adeleke

    Johnson Adeleke Active Member

    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 Hales

    Steve Hales ActEd Tutor Staff 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
     

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