# Markov Chains and Monte-Carlo Simulation

From IFORS Education Resources

**By: Volker Schmidt**

**Introduction**

- Markov chains

- are a fundamental class of stochastic models for sequences of non-independent random variables, i.e. of random variables possessing a specific dependency structure.

- have numerous applications e.g. in insurance and finance.

- play also an important role in mathematical modelling and analysis in a variety of other fields such as life sciences.

- Questions of scientific interest often exhibit a degree of complexity resulting in great difficulties if the attempt is made to find an adequate mathematical model that is solely based on analytical formulae.

- In these cases Markov chains can serve as an alternative analytical tool as they are crucial for the construction of computer algorithms for the Markov Chain Monte Carlo simulation (MCMC) of the mathematical models under consideration.

**Link to material:** http://www.mathematik.uni-ulm.de/stochastik/lehre/ss06/markov/skript_engl/