Solved problems on Markov chains

Markov chains have many applications, ranging from modeling communication networks to analyzing stock prices, Markov chains can be used in market research studies, they can model the probabilities of claims for insurance, they are used in the fields of public health and medicine, also they are used in ranking of websites in web searches. In general, Markov chains are particularly useful in modeling systems that have a finite number of states and transitions between those states and can be used to analyze and predict the long-term behavior of such systems.Most books on Markov chains are dedicated to reviewing theoretical concepts. The objective of this work is to make available to students and teachers a collection of solved problems on discrete-time Markov chains. In this sense, the work consists of solving 74 problems of different types. In them are obtained the transition probabilities and the transition matrix, the state spaces and the classes of those states, the n-step transition probabilities, the recurrence and transience, the invariant distributions, the mean return time and the convergence to equilibrium.

Autorentext

Alicia Corbacho. Graduate in Statistics. University of Extremadura, Spain. Fields of interest: Approximation theory, statistics and computer science. Specifically, topics related to intelligent driving, the approximation to the density and distribution functions of a random variable. The author has published some articles related to these topics.