This book considers the special class of random processes known as semi-Markov processes. These possess the Markov property with respect to any intrinsic Markov time such as the first exit time from an open set or a finite iteration of these times.
This class of semi-Markov processes includes strong Markov processes, Lévy and Smith stepped semi-Markov processes, as well as some other subclasses. Extensive coverage is devoted to non-Markovian semi-Markov processes with continuous trajectories and, in particular, to semi-Markov diffusion processes. Readers looking to enrich their knowledge on Markov processes will find this book an invaluable resource.
1. Stepped Semi-Markov Processes.
2. Sequences of the First Exit Times and regenerative times.
3. General Semi-Markov Processes.
4. Construction of Semi-Markov Processes using Semi-Markov Transition Functions.
5. Semi-Markov Processes of Diffusion Type.
6. Time Change and Semi-Markov Processes.
7. Limit Theorems for Semi-Markov Processes.
8. Represention of a Semi-Markov Process as a Transformed Markov Process.
9. Semi-Markov Model of Chromatography.
Boris Harlamov is Professor of Applied Mathematics and Informatics in the Department of Architecture and Building at the State University, St. Petersburg, Russia.