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Fix emphasis vs definitions in cake eating lectures
Changes per #721: - exogenous (cake_eating_egm.md) - adapted (cake_eating_stochastic.md) - state (cake_eating_stochastic.md) - control (cake_eating_stochastic.md) - topologically conjugate (cake_eating_time_iter.md) All terms changed from italic to bold as they are definitions per style guide.
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lectures/cake_eating_egm.md

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@@ -114,7 +114,7 @@ Let $(u')^{-1}$ be the inverse function of $u'$.
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The idea is this:
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* First, we fix an *exogenous* grid $\{k_i\}$ for capital ($k = x - c$).
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* First, we fix an **exogenous** grid $\{k_i\}$ for capital ($k = x - c$).
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* Then we obtain $c_i$ via
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```{math}

lectures/cake_eating_stochastic.md

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@@ -164,13 +164,13 @@ In summary, the agent's aim is to select a path $c_0, c_1, c_2, \ldots$ for cons
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1. nonnegative,
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1. feasible in the sense of {eq}`outcsdp0`,
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1. optimal, in the sense that it maximizes {eq}`texs0_og2` relative to all other feasible consumption sequences, and
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1. *adapted*, in the sense that the action $c_t$ depends only on
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1. **adapted**, in the sense that the action $c_t$ depends only on
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observable outcomes, not on future outcomes such as $\xi_{t+1}$.
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In the present context
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* $x_t$ is called the *state* variable --- it summarizes the "state of the world" at the start of each period.
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* $c_t$ is called the *control* variable --- a value chosen by the agent each period after observing the state.
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* $x_t$ is called the **state** variable --- it summarizes the "state of the world" at the start of each period.
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* $c_t$ is called the **control** variable --- a value chosen by the agent each period after observing the state.
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### The Policy Function Approach
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lectures/cake_eating_time_iter.md

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@@ -237,7 +237,7 @@ whenever $\sigma \in \mathscr P$.
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It is possible to prove that there is a tight relationship between iterates of
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$K$ and iterates of the Bellman operator.
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Mathematically, the two operators are *topologically conjugate*.
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Mathematically, the two operators are **topologically conjugate**.
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Loosely speaking, this means that if iterates of one operator converge then
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so do iterates of the other, and vice versa.

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