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Fix typos in kesten_process.rst #780

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7917a8f
Proofread and typo fix in heavy_tails
mtiley Nov 28, 2019
05f1caa
Fix typos in kesten_processes.rst
mtiley Nov 28, 2019
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10 changes: 5 additions & 5 deletions source/rst/heavy_tails.rst
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Expand Up @@ -64,7 +64,7 @@ It matters for taxation and redistribution
policies, as well as for flow-on effects for productivity growth, business
cycles, and political economy

* see, e.g., :cite:`acemoglu2002political`, :cite:`glaeser2003injustice`, :cite:`bhandari2018inequality` or :cite:`ahn2018inequality`).
* see, e.g., :cite:`acemoglu2002political`, :cite:`glaeser2003injustice`, :cite:`bhandari2018inequality` or :cite:`ahn2018inequality`.

This lecture formalizes some of the concepts introduced above and reviews the
key ideas.
Expand Down Expand Up @@ -123,7 +123,7 @@ Heavy Tails in Asset Returns
Next let's look at some financial data.

Our aim is to plot the daily change in the price of Amazon (AMZN) stock for
the period 1st January 2015 to 1st November 2019,
the period from 1st January 2015 to 1st November 2019.

This equates to daily returns if we set dividends aside.

Expand Down Expand Up @@ -172,7 +172,7 @@ One impact of heavy tails is that sample averages can be poor estimators of
the underlying mean of the distribution.

To understand this point better, recall :doc:`our earlier discussion
<lln_clt>` of the Law of Large Numbers, which considered iid :math:`X_1,
<lln_clt>` of the Law of Large Numbers, which considered IID :math:`X_1,
\ldots, X_n` with common distribution :math:`F`

If :math:`\mathbb E |X_i|` is finite, then
Expand Down Expand Up @@ -395,7 +395,7 @@ Prove: If :math:`X` has a Pareto tail with tail index :math:`\alpha`, then
Exercise 3
----------

Repeat exercise 1, but replacing the three distributions (two normal, one
Repeat exercise 1, but replace the three distributions (two normal, one
Cauchy) with three Pareto distributions using different choices of
:math:`\alpha`.

Expand Down Expand Up @@ -425,7 +425,7 @@ phenomena.

To illustrate this fact in a simple way, let us consider an economy with
100,000 firms, an interest rate of ``r = 0.05`` and a corporate tax rate of
15%.
15\%.

Your task is to estimate the present discounted value of projected corporate
tax revenue over the next 10 years.
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4 changes: 2 additions & 2 deletions source/rst/kesten_processes.rst
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Expand Up @@ -55,7 +55,7 @@ Kesten Processes
single: Kesten processes; heavy tails


A **Kesten process** is a stochastic processes of the form
A **Kesten process** is a stochastic process of the form

.. math::
:label: kesproc
Expand Down Expand Up @@ -230,7 +230,7 @@ Since :math:`F^*` is stationary for the wealth process, this is just
Hence the fraction of households with wealth in :math:`[0, y]` is the same
next period as it is this period.

Since :math:`y` was chosen arbitrarily, the distribution is inchanged.
Since :math:`y` was chosen arbitrarily, the distribution is unchanged.


Conditions for Stationarity
Expand Down