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Integrating factors for SDEs

  1. Nov 9, 2012 #1
    Whenever I'm given a SDE problem that requires us to multiply both sides by an "integrating-factor", it's always given to us as a *Hint*. I would like to know how to come up with these integrating factors.

    Here's some examples:

    1) For the mean-reverting Ornstein-Uhlenbeck (OU) SDE [itex]dX_t = (m-X_t)dt+\sigma X_tdB(t)[/itex], the appropriate integrating factor is [itex]e^t[/itex].

    2) For the non-mean-reverting OU SDE [itex]dX_t = uX_tdt + \sigma dB_t[/itex], the integrating factor is [itex]e^{-ut}[/itex].

    3) For the SDE [itex]dX_t = udt + \sigma X_t dB_t[/itex], the integrating factor is [itex]e^{-\sigma B_t + \frac12 \sigma^2 t}[/itex].
  2. jcsd
  3. Nov 9, 2012 #2
    I suppose you are at the beginning of ODE course,so integrating factors will be discussed later on.
    I hope you will find interest in the attached material here.
    Last edited: Nov 9, 2012
  4. Nov 9, 2012 #3

    1) What attached material?
    2) I'm at the end of a financial mathematics course (stochastic calculus). Integrating factors are provided to us and we will never learn how to discover them. I want to learn how to do this -- they aren't going to teach this to me.
  5. Nov 9, 2012 #4
    The attached material concern ordinary differential equations.I suupose it is the same for stochastic.

    Attached Files:

    • IFM.pdf
      File size:
      82.2 KB
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