08-markov-chains.Rmd

# Markov chains

## Learning Objectives {-#objectives-markov-chains}

1. State the essential features of a Markov chain model.
2. State the Chapman-Kolmogorov equations that represent a Markov chain.
3. Calculate the stationary distribution for a Markov chain in simple cases.
4. Describe a system of frequency based experience rating in terms of a Markov chain and describe other simple applications.
5. Describe a time-inhomogeneous Markov chain model and describe simple applications.
6. Demonstrate how Markov chains can be used as a tool for modelling and how they can be simulated.

## Theory {-#theory-markov-chains}

**TO ADD THEORY ABOUT MARKOV CHAINS HERE**

## Features of a Markov chain model

## Chapman-Kolmogorov equations

## Stationary distribution for a Markov chain

## Frequency based experience rating

## Time-inhomogeneous Markov chain model

## Markov chains in modelling

### Simulating a Markov chain

## `R` Practice {-#practice-markov-chains}

**TO ADD R EXAMPLE ABOUT MARKOV CHAINS HERE**