Markov chains in lectures

[jlperla]

Most require:

• simulation from a distributional or discrete initial condition
• access to the transition probability distribution, sometimes just mat-vec, occasionally rows/columns
• access to the values associated with the discrete states
• Most are small which might even work best as statics. Otherwise, all are dense.
  Tauchen could be truncated and made banded with very little loss, but probably not crucial here.
• Could have "names" for states, which would be useful downstream for plotting, but not crucial.
• calculation and access to the stationary distribution

The lectures which those apply to include:

• https://julia.quantecon.org/dynamic_programming/ifp.html
• https://julia.quantecon.org/dynamic_programming/smoothing.html
• https://julia.quantecon.org/multi_agent_models/aiyagari.html
• https://julia.quantecon.org/multi_agent_models/arellano.html
• https://julia.quantecon.org/multi_agent_models/harrison_kreps.html
• https://julia.quantecon.org/multi_agent_models/markov_asset.html

Other notes
https://julia.quantecon.org/tools_and_techniques/finite_markov.html

• All of the main onces
• manually shows simulation with a categorical value switching between them each time.
• check for irreducibility and get communication classes
• check periodicity

https://julia.quantecon.org/multi_agent_models/lake_model.html

• This also calculates the forward forecast distribution iterating forward as a discrete system, and could allow exploring ergodicity for absorbing states/etc.

https://julia.quantecon.org/multi_agent_models/aiyagari.html

• Simulation
• Also indirectly through the DiscreteDP

https://julia.quantecon.org/dynamic_programming/discrete_dp.html

• Only indirectly through the DiscreteDP

Tauchen is used in:

• https://julia.quantecon.org/multi_agent_models/arellano.html
• https://julia.quantecon.org/tools_and_techniques/finite_markov.html
• https://julia.quantecon.org/multi_agent_models/markov_asset.html
• But I think that it could be written in 10-20 lines and copy/pasted if absolutely necessary.
• No other discretizations of continuous processes seem to be there

Dynamic Programming Squared lectures, all just need simulation

• https://julia.quantecon.org/dynamic_programming_squared/amss.html
• https://julia.quantecon.org/dynamic_programming_squared/lqramsey.html
• https://julia.quantecon.org/dynamic_programming_squared/opt_tax_recur.html

[jlperla]

• Tauchen functionality added by Reorganized interpolation and integration #370 but cannot replace the arellano/etc. until simulate is also moved over.