I have a measure $\mu^x$ which is the law of a random variable and depends on $x$. The specific situation I am thinking of is $\mu^x$ is the law of $X_t$, the solution of an SDE with $X_0=x$. If I consider $x \mapsto \mu^x$ as a measure-valued function, is there a notion of differentiation (possibly in a Frechet sense) for such functions?
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