Asymptotic behaviour of Markov processes with two time scales

Markov processes are interesting stochastic proceses with a wide range of applications. In this report we study Markov processes with two time scales where the difference between the time speed of the scales is asymptotically large. In such a situation the behaviour of the process can be estimated by substituting the "faster" process by its limiting process. We will introduce Markov processes and study in particular Markov processes with two time scales in the limit where one of the time scales is much faster than the other. Later we will prove statements about the behaviour for a general situation. Finally, two interesting applications of this scenario will be discussed.Electrical Engineering, Mathematics and Computer ScienceDelft Institute of Applied Mathematic