Generalized Semi-Markov Processes: Antimatroid Structure and Second-Order Properties

Continuity of Generalized Semi-Markov Processes

It is shown that sequences of generalized semi-Markov processes converge in the sense of weak convergence of random functions if associated sequences of defining elements (initial distributions, transition functions and clock time distributions) converge. This continuity or stability is used to obtain information about invariant probability measures. It is shown that there exists an invariant p...

ADK Entropy and ADK Entropy Rate in Irreducible- Aperiodic Markov Chain and Gaussian Processes

In this paper, the two parameter ADK entropy, as a generalized of Re'nyi entropy, is considered and some properties of it, are investigated. We will see that the ADK entropy for continuous random variables is invariant under a location and is not invariant under a scale transformation of the random variable. Furthermore, the joint ADK entropy, conditional ADK entropy, and chain rule of this ent...

The KTH Visit in Semi-Markov Processes

The theory of interactive generalized semi-Markov processes

In this paper we introduce the calculus of interactive generalized semi-Markov processes (IGSMPs), a stochastic process algebra which can express probabilistic timed delays with general distributions and synchronizable actions with zero duration, and where choices may be probabilistic, non-deterministic and prioritized. IGSMP is equipped with a structural operational semantics which generates s...

Numerical Analysis of Generalized Semi-Markov Processes

This paper present methodological results that allow the cost-effective numerical analysis of finite-state generalized semi-Markov processes (GSMPs) with exponential and deterministic events by an embedded general state space Markov chain (GSSMC). Key contributions constitute the formal proof that elements of the transition kernel of the GSSMC can always be computed by appropriate summation of ...