Simple derivations of properties of counting processes associated with Markov renewal processes

DOI10.1239/jap/1134587814zbMath1106.60069OpenAlexW2064699702MaRDI QIDQ5476146

Robin K. Milne, Frank G. Ball

Publication date: 29 June 2006

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/jap/1134587814

zbMATH Keywords

factorial momentsemi-Markovmatrix renewal functions

Mathematics Subject Classification ID

Markov renewal processes, semi-Markov processes (60K15) Continuous-time Markov processes on discrete state spaces (60J27) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Applications of Markov renewal processes (reliability, queueing networks, etc.) (60K20)

Related Items

Statistics of transitions for Markov chains with periodic forcing ⋮ Counting labeled transitions in continuous-time Markov models of evolution ⋮ Summary Statistics for Endpoint-Conditioned Continuous-Time Markov Chains

Cites Work

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• Markov chain models - rarity and exponentiality
• Dependability for systems with a partitioned state space: Markov and semi-Markov theory and computational implementation
• The number of visits to a subset of the state space by a discrete- parameter semi-Markov process
• Analysis of a counting process associated with a semi-Markov process: number of entries into a subset of state space
• Some renewal-theoretic investigations in the theory of sojourn times in finite semi-Markov processes
• Exceptional Paper—Markov Renewal Theory: A Survey
• On the exact distribution of observed open times in single ion channel models
• Continuous-time Markov chains in a random environment, with applications to ion channel modelling
• Clustering of Bursts of Openings in Markov and Semi-Markov Models of Single Channel Gating
• Empirical clustering of bursts of openings in markov and semi-markov models of single channel gating incorporating time interval omission
• Applied Probability and Queues
• An Introduction to the Theory of Point Processes
• The distributions of the apparent open times and shut times in a single channel record when brief events cannot be detected
• Some passage-time generating functions for discrete-time and continuous-time finite Markov chains
• On the moments of Markov renewal processes
• On the Matrix Renewal Function for Markov Renewal Processes
• Markov renewal theory
• On the dispersion index of a Markovian molecular clock