Markov Processes: Markov Chains, Poisson Processes, Brownian Motion
Nadiya Fink
Visiting Assistant Professor
Mathematics and Computer Science
Albion College
The Markov property indicates that, with knowledge of the current state, previous trajectories are irrelevant for predicting the probability of the future of a process. A Markov chain is a discrete-time stochastic (i.e. random) process possessing the Markov property. Probabilities and expected values on a Markov chain can be evaluated by a technique called First Step Analysis. An analogous technique can be applied to continuous-time processes. We will discuss an elementary introduction to Markov chains and First Step Analysis, followed by a broader description and discussion of the long-term behavior of Markov chains. Further, we will get acquainted with the Poisson Processes which are continuous-time processes with finite number of states, and, finally, will overview the continuous processes and their applications.