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velcher t1_ir5und6 wrote

Thanks for the post!

In the section: Marginals of the time-changed OU-process

> The empirical measure \hat\mu = 1/J \sum_{j=1}^J \delta_{x_i}

  • What is \delta_{x_i}? It doesn't seem to be mentioned before. Is this just the difference between the J samples x^j?
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jakiwjakiw OP t1_ir6k6b9 wrote

The delta's stand are point measures. \delta_x has mass 1 at the point x and 0 everywhere else.
Therefore \hat\mu is the measure that has mass 1/J at each x_j and 0 everywhere else.

These point measures are also called "dirac delta" and the notation using the delta is common in my field, but it is rather confusing to just use them like that without explanation, thanks a lot for pointing that out. Will update that!

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