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Query regarding existence and uniqueness of SDE solutions

  1. Aug 18, 2011 #1

    yip

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    Hi,

    Just wanted to ask a question regarding existence and uniqueness of solutions to SDEs. Say you have shown existence and uniqueness of a solution to an SDE that the process [tex ] X_{t} [/tex ]a particular process follows (by showing drift and diffusion coefficients are Lipschitz). If you take a one to one transformation of the process, lets say, exponentiating it, do we have existence and uniqueness of a solution to the new SDE that the transformed process follows? The reason I am asking is because I am trying to show existence and uniqueness of a solution to the Black Karasinski model for interest rates, where the log of the short rate follows an Ornstein Uhlenbeck process. Existence and uniqueness is simple to show if you look at the SDE the log of the short rate follows, but if you use Ito's Lemma to derive the SDE that the short rate follows, then showing the coefficients are Lipschitz seems to be substantially more difficult.

    Thanks
     
  2. jcsd
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