In this paper, finite phase semi-Markov processes are introduced. By introducing variables and a simple transformation, every finite phase semi-Markov process can be transformed to a finite Markov chain which is called its associated Markov chain. A consequence of this is that every phase semi-Markovian switching system may be equivalently expressed as its associated Markovian switching system....

We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately repr...

Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process’ intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical complexity of stochastic processes generated by finite unifilar hidden semi-Markov models—memoryful, state-dependent versions of renewal processes. Calculati...

Stochastic processes with semi-Markov switches (or in semi-Markov environment) and general Switching processes are considered. In case of asymptotically ergodic environment functional Averaging Principle and Diiusion Approximation types theorems for trajectory of the process are proved. In case of asymptotically consolidated environment a convergence to a solution of a diierential or stochas-ti...

Information security incidents frequency has been increasing dramatically, the aim of this study is to analyze the state-space reachability problems through the transition of vulnerable status after the informative system vulnerability exposure. In this research we took into consideration the time factor to analyze the arrival time to reachable states problem discussed in stochastic Petri nets....

First-passage time densities and quantiles are important metrics in performance analysis. They are used in the analysis of mobile communication systems, web servers, manufacturing systems as well as for the analysis of the quality of service of hospitals and government organisations. In this report we look at computational techniques for the first-passage time analysis on highlevel models that ...

The paper examines the application of semi-Markov models to the phenomenon of earthquakes in Tehran province. Generally, earthquakes are not independent of each other, and time and place of earthquakes are related to previous earthquakes; moreover, the time between earthquakes affects the pattern of their occurrence; thus, this occurrence can be likened to semi-Markov models. ...