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Is there an equivalent of martingale representation theorem for Levy processes in some form? I believe there is no such theorem in generality, but maybe there are some specific versions?

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    @Grzenio: a propos cross posting, I know it is not in the FAQ (that's partly why I split into two comments instead of just one). Hence I explained it to you above in the comments why your question is closed.2011-07-26

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you might want to check out Theorem 61 in Protter's book about stochastic integration, but this covers only processes, that solve some affine SDE.