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gradstudent
gradstudent
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I am quite puzzled by the expression given in equation 21 (page 2110) in this paper, https://arxiv.org/pdf/1802.09188.pdf

Its LHS seems to be a measure $\nu_n^N$ and hence I guess it takes as argument measurable sets. Equation 21 is defining the measure $\nu_n^N$.

But its RHS is weighted sum of products of a measure $\mu_0$ and Markov kernels $R_{\gamma_i}$ As defined in its own equation 12, $R_\gamma$s are standard Markov kernels which needs 2 arguments a point and a measurable set.

  • So how is one to read this equation?

  • Is there a context to these kinds of expressions, that I am missing? Like, is this a familiar construction in some scenario? It would be great to get some pedagogic reference as to from where has this come!

I am quite puzzled by the expression given in equation 21 (page 21) in this paper, https://arxiv.org/pdf/1802.09188.pdf

Its LHS seems to be a measure $\nu_n^N$ and hence I guess it takes as argument measurable sets. Equation 21 is defining the measure $\nu_n^N$.

But its RHS is weighted sum of products of a measure $\mu_0$ and Markov kernels $R_{\gamma_i}$ As defined in its own equation 12, $R_\gamma$s are standard Markov kernels which needs 2 arguments a point and a measurable set.

  • So how is one to read this equation?

  • Is there a context to these kinds of expressions, that I am missing? Like, is this a familiar construction in some scenario? It would be great to get some pedagogic reference as to from where has this come!

I am quite puzzled by the expression given in equation 21 (page 10) in this paper, https://arxiv.org/pdf/1802.09188.pdf

Its LHS seems to be a measure $\nu_n^N$ and hence I guess it takes as argument measurable sets. Equation 21 is defining the measure $\nu_n^N$.

But its RHS is weighted sum of products of a measure $\mu_0$ and Markov kernels $R_{\gamma_i}$ As defined in its own equation 12, $R_\gamma$s are standard Markov kernels which needs 2 arguments a point and a measurable set.

  • So how is one to read this equation?

  • Is there a context to these kinds of expressions, that I am missing? Like, is this a familiar construction in some scenario? It would be great to get some pedagogic reference as to from where has this come!

Source Link
gradstudent
gradstudent
  • 2.2k
  • 16
  • 28

Defining measures through products of Markov kernels

I am quite puzzled by the expression given in equation 21 (page 21) in this paper, https://arxiv.org/pdf/1802.09188.pdf

Its LHS seems to be a measure $\nu_n^N$ and hence I guess it takes as argument measurable sets. Equation 21 is defining the measure $\nu_n^N$.

But its RHS is weighted sum of products of a measure $\mu_0$ and Markov kernels $R_{\gamma_i}$ As defined in its own equation 12, $R_\gamma$s are standard Markov kernels which needs 2 arguments a point and a measurable set.

  • So how is one to read this equation?

  • Is there a context to these kinds of expressions, that I am missing? Like, is this a familiar construction in some scenario? It would be great to get some pedagogic reference as to from where has this come!