Continuous semi Markovian processes. (Q2776776)

The monograph is devoted to a general class of càdlàg stochastic processes with values in a metric space. A process is called (generalized) semi-Markov process if it enjoys the Markov property w.r.t.\ the so-called `interior' stopping times such as the first exit time from an open subset. Semi-Markov processes contain a class of conventional step semi-Markov processes as well as all strong Markov processes. The book mainly deals with the theoretical approaches to semi-Markov processes and focuses on non-Markov semi-Markov processes with continuous trajectories. NEWLINENEWLINENEWLINEThe book consists of nine chapters. Chapter 1 contains basic facts about the step semi-Markov processes. Chapter 2 introduces embedded point processes of first exit times from the sequence of subsets of a metric space, and regeneration times. General semi-Markov processes are studied in Chapter 3. In Chapter 4, a semi-Markov process with prescribed family of semi-Markov transition functions is constructed. Chapter 5 is devoted to semi-Markov processes of diffusion type. They can be described with the help of elliptic differential equations. Chapter 6 studies the path properties of the process w.r.t.\ the time change. In Chapter 7, conditions for the weak convergence of step semi-Markov processes to a generalized semi-Markov process are considered. The representation of a semi-Markov process in terms of an appropriate time change of some Markov process is obtained in Chapter 8. Finally, Chapter 9 treats the semi-Markov model of chromatography. The bibliography contains 143 entries. The foundations of Markov processes are a prerequisite for the reader.