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

    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?

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