Hidden Markov Models
By: Ramon van Handel
The Markov property guarantees that the future evolution of the process depends only on its present state, and not on its past history. Markov processes are ubiquitous in stochastic modeling, and for good reasons. On the one hand, many models are naturally expected to be Markovian. For example, the basic laws of physics guarantee that the motion of a particle in a (small) time step is determined only by its present position and velocity; it does not matter how it ended up in this situation. On the other hand, the simple structure of Markov processes allow us to develop powerful mathematical techniques and computational algorithms which would be intractable without the Markov property. It is therefore very desirable in practice to build stochastic models which possess the Markov property.
Link to material: http://www.princeton.edu/~rvan/orf557/hmm080728.pdf