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Remove duplicate section in mccall_fitted_vfi.md
Removed a duplicated section that repeated the Bellman operator explanation and P operator definitions. The section starting with "In the discrete case, we ended up iterating on the Bellman operator" was appearing twice (lines 97-135 and 140-177), along with a duplicate "### Fitting" header. Removed the duplicate at lines 140-177, keeping only the first occurrence. 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude <[email protected]>
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lectures/mccall_fitted_vfi.md

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@@ -135,47 +135,6 @@ where $\psi$ is the standard normal density.
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Here we are thinking of $v_u$ as a function on all of $\RR_+$.
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### Fitting
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In the {doc}`discrete case <mccall_model_with_sep_markov>`, we ended up iterating on the Bellman operator
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$$
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(Tv_u)(w) =
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\max
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\left\{
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\frac{1}{1-\beta(1-\alpha)} \cdot
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\left(
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u(w) + \alpha\beta (Pv_u)(w)
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\right),
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u(c) + \beta(Pv_u)(w)
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\right\}
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$$
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where
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$$
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(P v_u)(w) := \sum_{w'} v_u(w') P(w, w')
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$$
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Here we iterate on the same law after changing the definition of the $P$ operator to
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$$
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(P v_u)(w) := \int v_u(w') p(w, w') d w'
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$$
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where $p(w, \cdot)$ is the conditional density of $w'$ given $w$.
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We can write this more explicitly as
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$$
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(P v_u)(w) := \int v_u( w^\rho \exp(\nu z) ) \psi(z) dz,
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$$
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where $\psi$ is the standard normal density.
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Here we are thinking of $v_u$ as a function on all of $\RR_+$.
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### Fitting
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In theory, we should now proceed as follows:

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