This title considers the special 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. The class of semi-Markov processes includes strong Markov processes, Levy and Smith stepped semi-Markov processes, and 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 a valuable resource.
Boris Harlamov is Professor of Applied Mathematics and Informatics in the Department of Architecture and Building at the State University, St. Petersburg, Russia.
Chapter 1. Stepped Semi-Markov Processes. Chapter 2. Sequences of the First Exit Times and Regenerative Times. Chapter 3. Semi-Markov Processes of General Type. Chapter 4. Construction of the Process with Semi-Markov Transition Functions. Chapter 5. Semi-Markov Processes of Diffusion Type. Chapter 6. Time Change and Semi-Markov Processes. Chapter 7. Limit Theorems for Semi-Markov Processes. Chapter 8. Representing of the Semi-Markov Process as a Transformed Markov Process. Chapter 9. Semi-Markov Model of Chromatography. List of Authors. Index.